Quick recall · 262 cards
Short MCQ-style retrieval prompts. Tap a card to reveal the answer.
PYQ
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Which one of the following is not a cube number? a) 1 b) 27 c) 64 d) 125
C · 64
PYQ
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Identify the pattern and find the missing number in the series: 1, 8, 9, 64, ?
A · 27
PYQ
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Find the number which would come in place of the question mark: 1, 7, 37, 187, 937, ?
A · 4687
PYQ
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Complete the number series: 2, 4, 8, 16, 32, ? Which type of series is this?
B · 64, GP
PYQ
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Which number is divisible by 2? 75, 45, 46, 49
C · C. 46
PYQ
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Which number is divisible by 4? 34, 51, 68, 38
C · C. 68
PYQ
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Maria paid $28 for a jacket that was discounted by 30%. What was the original price of the jacket? A) $36 B) $47 C) $40 D) $42.50
C · $40
Discount of 30% means she paid 70% of original price. Let original price be \( P \). Then \( 0.70P = 28 \). Solving: \( P = \frac{28}{0.70} = 40 \). Option C is $40, which matches the calculation.
PYQ · 2023
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A shopkeeper bought an oven for 225,000 and sold it for 229,500. He spent 21,500 as overheads. What is his loss or gain percentage (rounded off to the nearest integer)?
C · 6.25% loss
PYQ
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A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
C · Rs. 698
PYQ
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₹2,500, when invested for 8 years at a given rate of simple interest per year, amounted to ₹3,725 on maturity. What was the rate of simple interest that was paid per annum?
B · 6%
PYQ · 2023
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SSC CHSL 08/08/2023 (4th Shift): A certain sum amounts to Rs. 790 in 2 years and Rs. 910 in 3 years at simple interest. What is the rate of interest per annum?
A · 19%
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Which of the following is a natural number?
C · 7
Natural numbers are positive integers starting from 1, so 7 is a natural number.
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Which set of numbers includes zero?
B · Whole numbers
Whole numbers include zero and all natural numbers.
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Which of the following is an irrational number?
B · \( \sqrt{2} \)
\( \sqrt{2} \) is an irrational number because it cannot be expressed as a ratio of two integers.
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Which number type does \( -7 \) belong to?
C · Integer
−7 is an integer because integers include negative and positive whole numbers including zero.
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Which of the following best classifies the number \( 0.333\ldots \)?
B · Rational
0.333... is a repeating decimal and can be expressed as \( \frac{1}{3} \), so it is rational.
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Which of the following is NOT a composite number?
C · 17
17 is a prime number, not composite, as it has only two factors: 1 and 17.
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Which property states that \( a + b = b + a \) for any numbers \( a \) and \( b \)?
C · Commutative property
The commutative property states that changing the order of numbers does not change the sum or product.
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Which of the following is the multiplicative identity?
B · 1
1 is the multiplicative identity because any number multiplied by 1 remains unchanged.
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If \( a \) and \( b \) are integers, which property justifies \( a + (b + c) = (a + b) + c \)?
B · Associative property
The associative property states that the grouping of numbers does not affect the sum or product.
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Which property is illustrated by \( a \times (b + c) = a \times b + a \times c \)?
A · Distributive property
This is the distributive property of multiplication over addition.
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Which of the following numbers is both prime and odd?
C · 11
11 is a prime number and is odd. 2 is prime but even, 9 and 15 are composite.
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Identify the number type of \( -\frac{5}{3} \).
B · Rational number
\( -\frac{5}{3} \) is a rational number because it is a ratio of two integers.
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Which of the following numbers is irrational?
A · \( \pi \)
\( \pi \) is irrational because it cannot be expressed as a ratio of two integers.
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Which of the following is NOT an integer?
C · 4.5
4.5 is not an integer because integers are whole numbers without fractional parts.
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Which number type does the decimal 0.1010010001... (non-repeating) belong to?
B · Irrational
A non-repeating, non-terminating decimal is irrational.
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Which of the following numbers is a perfect square integer?
A · \( \sqrt{16} \)
\( \sqrt{16} = 4 \), which is a perfect square integer.
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Which of the following is the odd one out based on number type?
D · 9.5
9.5 is not an integer or natural number; it is a rational decimal, unlike the others which are prime or natural numbers.
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Calculate \( 3 + \frac{1}{2} \). What type of number is the result?
B · Rational number
The sum is \( \frac{7}{2} \), a rational number but not an integer.
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What is the result of multiplying a rational number by an irrational number?
C · Sometimes rational, sometimes irrational
The product can be rational or irrational depending on the numbers involved.
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If \( a = 5 \) (integer) and \( b = \sqrt{2} \) (irrational), what is \( a \times b \)?
C · Irrational number
Multiplying an integer by an irrational number results in an irrational number.
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Which of the following operations always results in an integer?
B · Difference of two integers
The difference of two integers is always an integer.
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What is the sum of the first five prime numbers?
A · 28
First five primes are 2, 3, 5, 7, 11; sum = 28.
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If \( x = 2 \) (whole number) and \( y = \frac{3}{4} \) (rational), what is \( x + y \)?
C · Rational number
Sum of whole number and rational number is rational.
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A number is divisible by 2 and 3 but not by 5. Which of the following could it be?
B · 12
12 is divisible by 2 and 3 but not by 5.
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If the product of two numbers is irrational, which of the following must be true?
B · One number is irrational and the other rational (nonzero)
Multiplying a nonzero rational number by an irrational number results in an irrational number.
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Which of the following is a prime factorization of 84?
A · 2 \times 2 \times 3 \times 7
84 = 2 \times 2 \times 3 \times 7 is the correct prime factorization.
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A rational number \( \frac{p}{q} \) is such that \( p \) and \( q \) are integers with no common factors other than 1. What is this form called?
A · Simplest form
When numerator and denominator have no common factors other than 1, the fraction is in simplest form.
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If \( x \) is a composite number between 10 and 20, which of the following could be \( x \)?
C · 15
15 is composite; 11, 13, and 17 are prime numbers.
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Which of the following is an example of an irrational number used in real-world applications?
A · \( \pi \) in calculating circle circumference
\( \pi \) is irrational and commonly used in geometry and engineering.
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Which of the following numbers is an irrational number?
B · \( \sqrt{2} \)
An irrational number cannot be expressed as a ratio of two integers. \( \sqrt{2} \) is a classic example of an irrational number.
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Identify the set to which the number \(-5\) belongs.
C · Integers
Natural numbers and whole numbers are non-negative. \(-5\) is a negative integer, so it belongs to the set of integers.
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Which of the following is a whole number?
B · 0
Whole numbers include all natural numbers and zero, but no negative numbers or fractions.
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Which of the following numbers is a rational number but not an integer?
A · \(\frac{7}{3}\)
A rational number can be expressed as a fraction of two integers. \(\frac{7}{3}\) is rational but not an integer.
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Which of the following is NOT a real number?
D · \( 3 + 2i \)
Real numbers include all rational and irrational numbers. \(3 + 2i\) is a complex number, not a real number.
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Which number belongs to all of the following sets: natural numbers, whole numbers, integers, rational numbers, and real numbers?
B · 1
1 is a natural number, whole number, integer, rational number, and real number.
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Which of the following numbers is irrational?
C · \( \sqrt{3} \)
\( \sqrt{3} \) is irrational because it cannot be expressed as a ratio of two integers.
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Which of the following sets contains only prime numbers?
A · 2, 3, 5, 7
Only 2, 3, 5, and 7 are prime numbers. Others include composite or non-prime numbers.
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Which of the following numbers is composite?
C · 25
25 is composite because it has factors other than 1 and itself (5 × 5).
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Which number is a prime number?
B · 31
31 is prime because it has no divisors other than 1 and 31.
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Which of the following is a composite number?
C · 27
27 is composite because it can be factored as 3 × 9.
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Find the prime factorization of 84.
A · \( 2^2 \times 3 \times 7 \)
84 = 2 × 2 × 3 × 7 = \( 2^2 \times 3 \times 7 \).
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Which of the following is a factor of 36?
B · 6
6 divides 36 exactly (36 ÷ 6 = 6), so it is a factor.
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What is the least common multiple (LCM) of 4 and 6?
A · 12
LCM of 4 and 6 is 12, the smallest number divisible by both.
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Which of the following numbers is a multiple of both 3 and 5?
A · 15
15 is divisible by both 3 and 5.
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Find the greatest common divisor (GCD) of 48 and 60.
B · 12
The GCD of 48 and 60 is 12.
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Which of the following is a perfect cube?
A · 27
27 = 3^3, so it is a perfect cube.
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Which number is a perfect square?
A · 36
36 = 6^2, so it is a perfect square.
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Which of the following is a perfect cube but not a perfect square?
A · 64
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Which of the following numbers is a perfect square but not a perfect cube?
A · 81
81 = 9^2 is a perfect square but not a perfect cube.
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What is the face value of 7 in the number 4,379?
A · 7
Face value is the digit itself, which is 7.
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What is the place value of 7 in the number 4,379?
B · 70
7 is in the tens place, so its place value is 70.
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In the number 5,682, what is the place value of 6?
C · 600
6 is in the hundreds place, so its place value is 600.
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If the digit 3 in the number 3,254 is replaced by 8, what is the difference in place value?
A · 5,000
3 is in the thousands place (3,000), 8 is 8,000. Difference = 8,000 - 3,000 = 5,000.
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Which of the following numbers is even and divisible by 3?
B · 18
18 is even and divisible by 3.
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Which number is divisible by 9?
B · 243
Sum of digits of 243 is 2+4+3=9, divisible by 9, so 243 is divisible by 9.
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Which of the following numbers is odd and divisible by 5?
B · 55
55 ends with 5 and is odd, so it is divisible by 5 and odd.
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Which number is divisible by both 2 and 3 but not by 4?
C · 30
30 is divisible by 2 and 3 but not by 4.
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Which of the following numbers is correctly classified as a rational number?
C · \( \frac{5}{8} \)
\( \frac{5}{8} \) is a rational number as it can be expressed as a ratio of two integers.
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Which of the following is NOT a natural number?
B · 0
Natural numbers start from 1 upwards; 0 is not a natural number.
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Which of the following numbers is an integer but not a whole number?
B · -3
-3 is an integer but not a whole number because whole numbers are non-negative.
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Which of the following integers is NOT a perfect power (i.e., cannot be expressed as \(m^k\) for integers \(m > 1, k > 1\)) but has exactly 3 distinct prime factors and the product of its digits is a perfect cube?
B · 378
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Match the following integers with their correct number of distinct prime factors:
Column A:
1) 2310
2) 4620
3) 6930
4) 9240
Column B:
A) 4
B) 5
C) 6
D) 3
C · 1-B, 2-C, 3-C, 4-C
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If \(x\) is the smallest positive integer such that \(x\) is divisible by 9, 16, and 25, and the sum of the digits of \(x\) is equal to the number of distinct prime factors of \(x\), what is \(x\)?
B · 3600
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Find the number of positive integers less than 10,000 that are divisible by exactly two distinct primes.
A · 2016
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Which of the following numbers is a perfect square and also a perfect cube but NOT a perfect sixth power?
D · 15625
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If \(p\) and \(q\) are distinct primes such that \(p^2 + q^2 = 130\), which of the following pairs \((p,q)\) is correct?
C · (3, 11)
Step 1: Check each pair:
- (7,11): 7^2 + 11^2 = 49 + 121 = 170
- (5,11): 25 + 121 = 146
- (3,11): 9 + 121 = 130
- (2,11): 4 + 121 = 125
Step 2: Only (3,11) sum is 130.
Correct answer: (3,11).
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Which of the following integers is divisible by exactly three distinct primes and has a digit sum equal to the product of these primes?
A · 210
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If \(x\) is a positive integer such that \(x^2\) has exactly 7 distinct prime factors, what is the minimum number of distinct prime factors of \(x\)?
D · 7
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Which of the following numbers is NOT divisible by the square of any prime factor it has?
C · 385
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If \(N\) is a positive integer such that \(N\) is divisible by 2, 3, and 5 but not by 7, and the sum of the digits of \(N\) is 15, which of the following could be \(N\)?
D · 270
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Find the smallest positive integer \(k\) such that \(k\) has exactly 4 distinct prime factors, and \(k + 1\) is a perfect square.
A · 210
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Which of the following best defines divisibility of an integer \(a\) by another integer \(b\)?
A · When \(a\) divided by \(b\) leaves a remainder zero
An integer \(a\) is divisible by \(b\) if \(a\) divided by \(b\) leaves no remainder.
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If a number is divisible by 2 and 3, which of the following must it also be divisible by?
B · 6
If a number is divisible by both 2 and 3, it is divisible by their least common multiple, which is 6.
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Which of the following statements is true about divisibility?
B · 0 is divisible by every non-zero number
0 divided by any non-zero number is 0 with no remainder, so 0 is divisible by every non-zero number.
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Which of the following numbers is divisible by 2 but not by 5?
C · 62
62 is even, so divisible by 2, but does not end with 0 or 5, so not divisible by 5.
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Which of the following numbers is divisible by 9?
A · 729
Sum of digits of 729 is 7+2+9=18, which is divisible by 9, so 729 is divisible by 9.
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Which of the following numbers is divisible by both 3 and 5?
A · 45
45 is divisible by 3 (sum of digits 4+5=9) and ends with 5, so divisible by 5.
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A number is divisible by 10 if it ends with which digit?
A · 0
Numbers ending with 0 are divisible by 10.
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Which of the following numbers is divisible by 4?
A · 312
A number is divisible by 4 if its last two digits form a number divisible by 4. Here, 12 is divisible by 4.
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Which of the following numbers is divisible by 11?
A · 2728
For divisibility by 11, difference between sum of digits in odd and even places is multiple of 11 or zero. For 2728: (2+2) - (7+8) = 4 - 15 = -11, divisible by 11.
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Which of the following numbers is divisible by 8?
A · 1024
A number is divisible by 8 if its last three digits form a number divisible by 8. 024 (24) is divisible by 8.
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Which of the following numbers is divisible by 6 but not by 4?
A · 54
54 is divisible by 6 (divisible by 2 and 3) but last two digits (54) are not divisible by 4.
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Which of the following numbers is divisible by 12?
A · 144
A number divisible by both 3 and 4 is divisible by 12. 144 is divisible by 3 and 4.
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Find the highest common factor (HCF) of 36 and 48.
B · 12
Factors of 36: 1,2,3,4,6,9,12,18,36; Factors of 48: 1,2,3,4,6,8,12,16,24,48. Highest common factor is 12.
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What is the least common multiple (LCM) of 8 and 12?
A · 24
Multiples of 8: 8,16,24,32... Multiples of 12: 12,24,36... LCM is 24.
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If \(a = 2^3 \times 3^2\) and \(b = 2^2 \times 3^3\), what is the HCF of \(a\) and \(b\)?
A · \(2^2 \times 3^2\)
HCF takes the minimum powers of common prime factors: \(2^2\) and \(3^2\).
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Find the LCM of 15 and 20 using prime factorization.
A · 60
15 = 3 \times 5, 20 = 2^2 \times 5; LCM = 2^2 \times 3 \times 5 = 60.
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A number is divisible by 3 and 4 but not by 6. Which of the following could be the number?
D · None of these
If a number is divisible by 3 and 4, it must be divisible by 6 (since 6 = 2 \times 3). So no such number exists.
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The product of two numbers is 180 and their HCF is 6. What is their LCM?
A · 30
Product of two numbers = HCF \(\times\) LCM. So, LCM = \(\frac{180}{6} = 30\).
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A number leaves a remainder 3 when divided by 4, and remainder 4 when divided by 5. What is the smallest such number?
A · 19
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Which of the following numbers is divisible by 9 but not by 3?
D · None of these
If a number is divisible by 9, it is always divisible by 3. So no such number exists.
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A number is divisible by 2, 3, and 5. Which of the following is the smallest such number?
C · 30
The smallest number divisible by 2, 3, and 5 is their LCM = 30.
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If \(x\) is divisible by 4 and 6, but not by 12, which of the following could be \(x\)?
D · None of these
If \(x\) is divisible by 4 and 6, it must be divisible by 12 (LCM of 4 and 6). So no such \(x\) exists.
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The sum of digits of a number is 27. Which of the following numbers could be divisible by 9?
D · All of these
If the sum of digits is divisible by 9, the number is divisible by 9. Here, 27 is divisible by 9, so all options are divisible by 9.
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Which of the following is a prime number?
C · 53
53 has no divisors other than 1 and itself, so it is prime.
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Which of the following is a perfect square?
B · 64
64 = 8^2, so it is a perfect square.
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Which of the following numbers is composite?
D · 35
35 has factors other than 1 and itself (5 and 7), so it is composite.
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Which of the following numbers is both a perfect square and divisible by 9?
A · 81
81 = 9^2 and divisible by 9.
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Which of the following numbers is NOT divisible by 11?
C · 154
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Which of the following numbers is NOT divisible by 11?
C · 157
157: sum of digits at odd places = 1 + 7 = 8; even place = 5; difference = 3, not divisible by 11.
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Which of the following best defines divisibility of integers?
C · An integer \(a\) is divisible by \(b\) if \(a \div b\) leaves no remainder
Divisibility means that when \(a\) is divided by \(b\), the remainder is zero.
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If a number is divisible by 4, which of the following must be true?
B · Its last two digits form a number divisible by 4
A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
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Which of the following numbers is divisible by 6?
A · 132
A number is divisible by 6 if it is divisible by both 2 and 3. 132 is even and sum of digits (1+3+2=6) is divisible by 3.
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Which of the following statements is true about divisibility?
A · If \(a\) divides \(b\) and \(b\) divides \(c\), then \(a\) divides \(c\)
Divisibility is transitive: if \(a|b\) and \(b|c\), then \(a|c\).
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Which of the following numbers is divisible by 9?
A · 729
A number is divisible by 9 if the sum of its digits is divisible by 9. Sum of digits of 729 is 7+2+9=18, which is divisible by 9.
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Which of the following numbers is divisible by both 2 and 5?
A · 150
A number divisible by both 2 and 5 must be divisible by 10, so it ends with 0. 150 ends with 0.
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A number is divisible by 8 if:
A · Its last three digits form a number divisible by 8
A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
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Which of the following numbers is divisible by 3 but not by 9?
A · 123
123 has digit sum 1+2+3=6 divisible by 3 but not by 9. 135, 729, and 99 are divisible by 9.
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If a number is divisible by 2 and 3, which of the following must be true?
B · It is divisible by 6
If a number is divisible by both 2 and 3, it is divisible by their LCM, which is 6.
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Which of the following numbers is NOT divisible by 10?
C · 125
A number divisible by 10 ends with 0. 125 ends with 5, so it is not divisible by 10.
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If \(a\) divides \(b\) and \(a\) divides \(c\), which of the following is always divisible by \(a\)?
C · Both \(b + c\) and \(b - c\)
If \(a|b\) and \(a|c\), then \(a\) divides both \(b + c\) and \(b - c\).
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If 7 divides \(x - y\) and 7 divides \(y - z\), which of the following is true?
B · 7 divides \(x - z\)
Since 7 divides both \(x - y\) and \(y - z\), it divides their sum \((x - y) + (y - z) = x - z\).
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If \(a\) divides \(b\) and \(b\) divides \(c\), which of the following statements is false?
B · \(b\) divides \(a\)
\(b\) dividing \(a\) is not guaranteed by \(a\) dividing \(b\).
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Which of the following is a factor of 84?
A · 7
7 divides 84 exactly since \(84 \div 7 = 12\).
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Which of the following is a multiple of 12?
A · 96
96 is divisible by 12 since \(12 \times 8 = 96\).
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Find the greatest common factor (GCF) of 36 and 48 using their factors.
B · 12
Factors of 36: 1,2,3,4,6,9,12,18,36; Factors of 48: 1,2,3,4,6,8,12,16,24,48. Greatest common factor is 12.
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Which of the following numbers is NOT a multiple of 15?
C · 88
88 is not divisible by 15 since \(88 \div 15\) leaves a remainder.
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Which of the following is the least common multiple (LCM) of 4 and 6?
A · 12
LCM of 4 and 6 is 12, the smallest number divisible by both.
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What is the prime factorization of 90?
A · \(2 \times 3^2 \times 5\)
90 = 2 \times 3 \times 3 \times 5 = \(2 \times 3^2 \times 5\).
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If the prime factorization of a number is \(2^3 \times 3^2\), which of the following numbers divides it?
C · 36
The number is \(2^3 \times 3^2 = 8 \times 9 = 72\). 48 = \(2^4 \times 3\) which does not divide 72. 36 = \(2^2 \times 3^2\) divides 72, 54 = \(2 \times 3^3\) does not divide 72. Correct answer is 36.
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Which of the following numbers is prime?
A · 29
29 has no divisors other than 1 and itself, so it is prime.
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If the prime factorization of 210 is \(2 \times 3 \times 5 \times 7\), which of the following is NOT a factor of 210?
D · 45
45 = \(3^2 \times 5\), but 210 has only one 3, so 45 is not a factor.
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Find the HCF of 48 and 60 using prime factorization.
A · 12
48 = \(2^4 \times 3\), 60 = \(2^2 \times 3 \times 5\). Common factors: \(2^2 \times 3 = 12\).
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What is the LCM of 15 and 20?
A · 60
Prime factors: 15 = \(3 \times 5\), 20 = \(2^2 \times 5\). LCM = \(2^2 \times 3 \times 5 = 60\).
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If the HCF of two numbers is 6 and their LCM is 72, which of the following could be the numbers?
C · (18, 24)
Product of numbers = HCF \(\times\) LCM = 6 \(\times\) 72 = 432. 18 \(\times\) 24 = 432, so (18,24) fits.
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Which of the following is a perfect square number?
A · 121
121 = \(11^2\), so it is a perfect square.
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Which of the following is a cube number?
A · 64
64 = \(4^3\), so it is a cube number.
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Which of the following numbers is odd and divisible by 3?
A · 27
27 is odd and divisible by 3. Others are even.
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Which of the following numbers is NOT a perfect square?
D · 180
180 is not a perfect square; others are squares of 12, 13, and 14 respectively.
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What does 50% represent in terms of a fraction?
A · \( \frac{1}{2} \)
50% means 50 per 100, which is equivalent to \( \frac{50}{100} = \frac{1}{2} \).
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Which of the following is equivalent to 25%?
A · 0.25
25% means 25 per 100, which as a decimal is 0.25.
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If a quantity is increased by 100%, what will be the new quantity?
A · Double the original
An increase of 100% means the quantity becomes original + 100% of original = 2 times the original.
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What is 1% of 200?
A · 2
1% of 200 = \( \frac{1}{100} \times 200 = 2 \).
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Convert \( \frac{3}{5} \) to a percentage.
A · 60%
\( \frac{3}{5} = 0.6 = 60\% \).
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Which decimal is equivalent to 12.5%?
A · 0.125
12.5% = \( \frac{12.5}{100} = 0.125 \).
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Express 0.375 as a percentage.
A · 37.5%
0.375 = 37.5% because \( 0.375 \times 100 = 37.5\% \).
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Convert 7.5% to a fraction in simplest form.
A · \( \frac{3}{40} \)
7.5% = \( \frac{7.5}{100} = \frac{15}{200} = \frac{3}{40} \) in simplest form.
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Calculate 15% of 240.
A · 36
15% of 240 = \( \frac{15}{100} \times 240 = 36 \).
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Find 40% of 150.
A · 60
40% of 150 = \( \frac{40}{100} \times 150 = 60 \).
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What is 12.5% of 320?
A · 40
12.5% of 320 = \( \frac{12.5}{100} \times 320 = 40 \).
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Calculate 7.5% of 480.
A · 36
7.5% of 480 = \( \frac{7.5}{100} \times 480 = 36 \).
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What is 25% of 640 plus 10% of 320?
A · 240
25% of 640 = 160 and 10% of 320 = 32, sum = 192.
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A price of an article increases from \( \$120 \) to \( \$150 \). What is the percentage increase?
A · 25%
Percentage increase = \( \frac{150 - 120}{120} \times 100 = 25\% \).
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The population of a town decreases from 50,000 to 45,000. What is the percentage decrease?
A · 10%
Percentage decrease = \( \frac{50,000 - 45,000}{50,000} \times 100 = 10\% \).
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If the price of a product is reduced by 15%, what is the new price of an item originally priced at \( \$200 \)?
A · \( \$170 \)
New price = \( 200 - 15\% \times 200 = 200 - 30 = 170 \).
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A salary is increased by 10% and then decreased by 5%. What is the net percentage change in salary?
A · 4.5% increase
Net change = \( (1 + 0.10)(1 - 0.05) - 1 = 1.10 \times 0.95 - 1 = 1.045 - 1 = 0.045 = 4.5\% \) increase.
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A shopkeeper sells an article for \( \$540 \) after giving a 10% discount. What was the marked price?
A · \( \$600 \)
Let marked price = \( x \). After 10% discount, selling price = \( 0.9x = 540 \) \( \Rightarrow x = 600 \).
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A trader buys an article for \( \$400 \) and sells it for \( \$460 \). What is the profit percentage?
A · 15%
Profit = 460 - 400 = 60. Profit % = \( \frac{60}{400} \times 100 = 15\% \).
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An article is sold at a loss of 12.5%. If the selling price is \( \$350 \), what is the cost price?
A · \( \$400 \)
Selling price = 87.5% of cost price \( \Rightarrow 0.875 \times CP = 350 \Rightarrow CP = 400 \).
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A product is marked 20% above cost price. If a discount of 10% is given on the marked price, what is the profit percentage?
A · 8%
Marked price = 120% of cost price. Selling price = 90% of marked price = 0.9 \times 1.2 CP = 1.08 CP. Profit = 8%.
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An article is sold for \( \$540 \) after two successive discounts of 10% and 5%. What was the marked price?
A · \( \$630 \)
Let marked price = \( x \). Selling price = \( x \times 0.9 \times 0.95 = 0.855x = 540 \Rightarrow x = 540 / 0.855 = 630 \).
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A price is increased by 20% and then decreased by 10%. What is the net percentage change?
A · 8% increase
Net change = \( (1 + 0.20)(1 - 0.10) - 1 = 1.20 \times 0.90 - 1 = 1.08 - 1 = 0.08 = 8\% \) increase.
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If a quantity is decreased by 15% and then increased by 20%, what is the net percentage change?
A · 2% increase
Net change = \( (1 - 0.15)(1 + 0.20) - 1 = 0.85 \times 1.20 - 1 = 1.02 - 1 = 0.02 = 2\% \) increase.
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A price is increased by 25% and then decreased by 20%. What is the net percentage change in price?
A · 0% (no change)
Net change = \( (1 + 0.25)(1 - 0.20) - 1 = 1.25 \times 0.80 - 1 = 1.0 - 1 = 0 = 0\% \) no change.
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An article's price is first increased by 10% and then by 20%. What is the overall percentage increase?
A · 32%
Overall increase = \( (1 + 0.10)(1 + 0.20) - 1 = 1.1 \times 1.2 - 1 = 1.32 - 1 = 0.32 = 32\% \).
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If 30 is 60% of a number, what is the number?
A · 50
Let the number be \( x \). Then \( 0.6x = 30 \Rightarrow x = 50 \).
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What percent of 80 is 20?
A · 25%
Percentage = \( \frac{20}{80} \times 100 = 25\% \).
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If 15 is 30% of a number, what is 50% of that number?
A · 25
Number = \( \frac{15}{0.3} = 50 \). 50% of number = \( 0.5 \times 50 = 25 \).
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If \( x \)% of 60 is 18, find \( x \).
A · 30
\( \frac{x}{100} \times 60 = 18 \Rightarrow x = \frac{18 \times 100}{60} = 30 \).
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In a class of 80 students, 60% passed the exam. How many students failed?
A · 32
Passed = 60% of 80 = 48, so failed = 80 - 48 = 32.
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A survey shows that 40% of people prefer tea over coffee. If 120 people prefer tea, what is the total number of people surveyed?
A · 300
Total = \( \frac{120}{0.4} = 300 \).
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In a company, 25% of employees are women. If there are 150 women, how many employees are there in total?
A · 600
Total employees = \( \frac{150}{0.25} = 600 \).
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If 15% of a number is 45, what is 40% of the same number?
A · 120
Number = \( \frac{45}{0.15} = 300 \). 40% of number = \( 0.4 \times 300 = 120 \).
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The population of a town increases by 15% in the first year, decreases by 10% in the second year, and then increases by 20% in the third year. If the population after 3 years is 15,552, what was the original population?
A · 12,000
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A company’s profit increases by 40% in the first year and then decreases by 25% in the second year. If the profit at the end of the second year is Rs. 52,500, what was the profit at the beginning of the first year?
A · Rs. 50,000
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A quantity is increased by 50%, then decreased by 40%, and finally increased by 20%. What is the net percentage change in the quantity?
A · 14.4% increase
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A shopkeeper offers two successive discounts of 15% and 10% on the marked price of an article. If the shopkeeper still makes a profit of 12% on the cost price, what is the ratio of the cost price to the marked price?
A · 25:36
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A sum of Rs. 15,000 is lent out in two parts at 8% and 10% simple interest respectively. If the total interest earned in 3 years is Rs. 3,960, find the amount lent at 8%.
A · Rs. 9,000
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A price of an article is increased by 12.5% and then decreased by 20%. What is the net percentage change in price? Also, if the final price is Rs. 1,200, find the original price.
A · 5% decrease, Rs. 1,263.16
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A sum of money is divided among A, B, and C such that A gets 20% more than B and B gets 25% more than C. If the total sum is Rs. 21,000, find the amount received by A.
A · Rs. 8,400
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If the price of sugar increases by 12.5% and a family reduces its consumption by 10%, what is the net percentage change in expenditure on sugar?
A · 1.25% increase
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A quantity is increased by 30% and then decreased by 30%. What is the net percentage change in the quantity?
A · 9% decrease
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Which of the following best defines 'Profit' in profit and loss terminology?
C · When the selling price is more than the cost price
Profit occurs when the selling price (SP) of an item is greater than its cost price (CP).
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Loss occurs when:
C · SP < CP
Loss occurs when the selling price is less than the cost price.
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If the cost price and selling price of an article are equal, what is the profit or loss?
C · No profit, no loss
When cost price equals selling price, there is neither profit nor loss.
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A shopkeeper buys an article for \( \$200 \) and sells it for \( \$250 \). What is the profit?
A · \( \$50 \)
Profit = Selling Price - Cost Price = \( 250 - 200 = 50 \).
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If an article is sold at a loss of \( \$30 \) and the cost price is \( \$300 \), what is the selling price?
A · \( \$270 \)
Selling Price = Cost Price - Loss = \( 300 - 30 = 270 \).
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A trader bought an article for \( \$500 \) and sold it for \( \$450 \). What is the loss percentage?
A · 10%
Loss = \( 500 - 450 = 50 \). Loss % = \( \frac{50}{500} \times 100 = 10\% \).
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If the profit on an article is 20% and the cost price is \( \$400 \), what is the selling price?
A · \( \$480 \)
Profit = 20% of 400 = \( 0.20 \times 400 = 80 \). Selling Price = \( 400 + 80 = 480 \).
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An article is sold at a profit of 25%. If the selling price is \( \$250 \), what is the cost price?
A · \( \$200 \)
Let CP = \( x \). Then, SP = CP + 25% of CP = \( 1.25x = 250 \) \( \Rightarrow x = 200 \).
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If the loss percentage is 10% and the selling price is \( \$450 \), what is the cost price?
A · \( \$500 \)
Loss % = 10%, so SP = 90% of CP \( \Rightarrow 450 = 0.9 \times CP \Rightarrow CP = 500 \).
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If the marked price of an article is \( \$600 \) and the cost price is \( \$400 \), what is the profit percentage if the article is sold at the marked price?
A · 50%
Profit = \( 600 - 400 = 200 \). Profit % = \( \frac{200}{400} \times 100 = 50\% \).
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An article is marked at \( \$500 \) and sold at a 10% discount. If the cost price is \( \$400 \), what is the profit or loss percentage?
B · Profit of 12.5%
Selling Price = \( 500 - 10\% \times 500 = 450 \). Profit = \( 450 - 400 = 50 \). Profit % = \( \frac{50}{400} \times 100 = 12.5\% \).
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If the marked price is \( \$800 \) and the discount given is 20%, what is the selling price?
A · \( \$640 \)
Selling Price = Marked Price - Discount = \( 800 - 20\% \times 800 = 800 - 160 = 640 \).
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A shopkeeper marks an article 25% above the cost price and offers a discount of 10%. What is the net profit percentage?
A · 12.5%
Marked Price = \( 125\% \) of CP. Selling Price = \( 90\% \) of Marked Price = \( 0.9 \times 1.25 \times CP = 1.125 \times CP \). Profit % = \( 12.5\% \).
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If the cost price of an article is \( \$1000 \), the marked price is \( \$1200 \), and the discount given is 15%, what is the profit or loss percentage?
A · 2% profit
Selling Price = \( 1200 - 15\% \times 1200 = 1020 \). Profit = \( 1020 - 1000 = 20 \). Profit % = \( \frac{20}{1000} \times 100 = 2\% \).
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A shopkeeper sells an article for \( \$540 \) and gains 20%. What is the cost price?
A · \( \$450 \)
Let CP = \( x \). SP = \( 1.20x = 540 \) \( \Rightarrow x = 450 \).
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A trader sells two articles for \( \$400 \) each. On one, he gains 25%, and on the other, he loses 25%. What is his overall profit or loss percentage?
A · Loss of 6.25%
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A man buys an article for \( \$600 \) and sells it at a profit of 10%. He then buys another article for \( \$660 \) and sells it at a loss of 10%. What is his overall gain or loss?
A · Loss of \( \$6 \)
First SP = \( 600 + 10\% \times 600 = 660 \). Second SP = \( 660 - 10\% \times 660 = 594 \). Total CP = 1260, Total SP = 1254, loss = 6.
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A shopkeeper sells an article at a profit of 20%. If he had bought it for \( \$200 \) less, his profit would have been 40%. What is the cost price?
D · \( \$1400 \)
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A man sells two articles for \( \$1500 \) each. On one, he gains 20%, and on the other, he loses 20%. What is the overall gain or loss percentage?
A · Loss of 4%
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An article is sold at a profit of 10%. If the selling price is \( \$660 \), what was the cost price?
A · \( \$600 \)
Let CP = \( x \). SP = \( 1.1x = 660 \) \( \Rightarrow x = 600 \).
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A man buys an article for \( \$500 \) and sells it at a profit of 10%. He then buys another article for \( \$600 \) and sells it at a loss of 10%. What is his overall gain or loss?
A · Loss of \( \$10 \)
First SP = \( 500 + 10\% \times 500 = 550 \). Second SP = \( 600 - 10\% \times 600 = 540 \). Total CP = 1100, Total SP = 1090, loss = 10.
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If a man gains 20% on the first article and loses 20% on the second article, both sold for \( \$600 \), what is the overall profit or loss percentage?
D · Loss of 4%
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A shopkeeper sells an article at a profit of 25%. If the cost price was \( \$480 \), what is the selling price?
A · \( \$600 \)
Selling Price = \( 480 + 25\% \times 480 = 480 + 120 = 600 \).
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A trader sells two articles for \( \$450 \) each. On one, he gains 10%, and on the other, he loses 10%. What is his overall gain or loss percentage?
A · Loss of 1%
CP of first article = \( \frac{450}{1.1} = 409.09 \), CP of second article = \( \frac{450}{0.9} = 500 \). Total CP = 909.09, Total SP = 900, loss = 9.09, loss % = \( 1\% \).
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A man sells two articles for \( \$600 \) each. On one, he gains 15%, and on the other, he loses 15%. What is the overall gain or loss percentage?
A · Loss of 2.25%
CP of first article = \( \frac{600}{1.15} = 521.74 \), CP of second article = \( \frac{600}{0.85} = 705.88 \). Total CP = 1227.62, Total SP = 1200, loss = 27.62, loss % = \( 2.25\% \).
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A man buys an article for \( \$800 \) and sells it at a loss of 12.5%. He then sells another article for \( \$700 \) and gains 12.5%. What is his overall gain or loss?
A · Loss of \( \$25 \)
First SP = \( 800 - 12.5\% \times 800 = 700 \). Second SP = \( 700 + 12.5\% \times 700 = 787.5 \). Total CP = 1500, Total SP = 1487.5, loss = 12.5.
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A shopkeeper sells an article at a profit of 20%. If the cost price is \( \$500 \), what is the selling price after two successive profits of 10% each?
A · \( \$605 \)
After first 10% profit: \( 500 \times 1.10 = 550 \). After second 10% profit: \( 550 \times 1.10 = 605 \).
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An article is bought for \( \$1000 \). It is sold at a profit of 20%, then the profit is reinvested and another profit of 10% is earned on the new amount. What is the final amount?
A · \( \$1320 \)
After first profit: \( 1000 \times 1.20 = 1200 \). After second profit: \( 1200 \times 1.10 = 1320 \).
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A man sells an article at a loss of 10%. If he had sold it for \( \$20 \) more, he would have gained 5%. What is the cost price?
A · \( \$200 \)
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A man mixes two varieties of rice, one costing \( \$40 \) per kg and the other \( \$60 \) per kg. If he sells the mixture at \( \$50 \) per kg, what is the ratio in which the two varieties are mixed?
A · 1:1
Using allegation method: \( \frac{60 - 50}{50 - 40} = \frac{10}{10} = 1:1 \).
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A grocer mixes two varieties of sugar costing \( \$30 \) and \( \$40 \) per kg. In what ratio should he mix them to gain 20% by selling at \( \$48 \) per kg?
A · 3:2
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A shopkeeper mixes two types of tea costing \( \$20 \) and \( \$30 \) per kg in the ratio 3:2. If he sells the mixture at \( \$28 \) per kg, what is his profit or loss percentage?
B · Profit of 6%
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A shopkeeper marks his goods 25% above the cost price but allows a discount of 12% on the marked price. If he still makes a profit of ₹108 on selling 12 articles, what is the cost price per article?
A · ₹90
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A dealer sells an article at a profit of 20%. If he had bought it at 10% less and sold it for ₹50 less, his profit would have been 40%. What is the cost price of the article?
B · ₹300
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A shopkeeper sells an article at a loss of 12%. If he had sold it for ₹48 more, he would have gained 8%. Find the cost price of the article.
A · ₹240
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A man buys 40 articles for ₹2,400. He sells half of them at a profit of 20% and the other half at a loss of 10%. What is his overall profit or loss percentage?
A · 5% profit
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A shopkeeper mixes two types of tea costing ₹320/kg and ₹400/kg in the ratio 3:2. He sells the mixture at ₹420/kg. Find his profit percentage.
A · 20%
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A shopkeeper sells an article at a profit of 25%. If he had bought it for ₹40 less and sold it for ₹30 less, his profit would have been 50%. What is the original cost price of the article?
A · ₹160
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A trader marks his goods 40% above cost price and allows a discount of 15%. What is his profit percentage?
A · 19%
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A shopkeeper buys 60 articles at a total cost of ₹9,000. He sells one-third of them at a profit of 10%, one-third at a loss of 5%, and the rest at no profit no loss. What is his overall profit or loss percentage?
B · 1.67% loss
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A retailer buys 100 units of a product at ₹50 each and 150 units at ₹60 each. He sells all units at a uniform price and makes a profit of 20% on the total cost. What is the selling price per unit?
D · ₹68
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A trader sells an article at a profit of 25%. If he had bought it for ₹20 less and sold it for ₹10 less, his profit would have been 50%. Find the cost price of the article.
A · ₹80
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What is the correct formula for calculating Simple Interest (SI)?
A · \( SI = \frac{P \times R \times T}{100} \)
Simple Interest is calculated using the formula \( SI = \frac{P \times R \times T}{100} \), where P is principal, R is rate of interest per annum, and T is time in years.
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Simple Interest is calculated on which of the following amounts?
A · Principal only
Simple Interest is calculated only on the original principal amount throughout the time period.
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Which of the following represents the time period in the Simple Interest formula?
C · T
In the formula \( SI = \frac{P \times R \times T}{100} \), T represents the time period in years.
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If the principal is \( \$2000 \), rate of interest is 5% per annum, and time is 3 years, what is the Simple Interest?
A · \( \$300 \)
Using \( SI = \frac{P \times R \times T}{100} = \frac{2000 \times 5 \times 3}{100} = 300 \).
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Calculate the Simple Interest on a principal of \( \$1500 \) at 6% per annum for 4 years.
A · \( \$360 \)
SI = \( \frac{1500 \times 6 \times 4}{100} = 360 \).
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A sum of money amounts to \( \$1200 \) in 2 years at 5% simple interest. What is the principal amount?
C · \( \$1000 \)
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If the Simple Interest on a principal of \( \$2500 \) at 8% per annum is \( \$600 \), what is the time period in years?
A · 3 years
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A principal of \( \$1800 \) is invested at a rate of 7.5% per annum. How much interest will be earned in 2.5 years?
A · \( \$337.50 \)
SI = \( \frac{1800 \times 7.5 \times 2.5}{100} = 337.50 \).
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Which of the following correctly expresses the relationship between Principal (P), Rate (R), Time (T), and Simple Interest (SI)?
A · \( SI \propto P \), \( SI \propto R \), \( SI \propto T \)
Simple Interest is directly proportional to Principal, Rate, and Time individually.
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If the principal doubles, keeping rate and time constant, what happens to the Simple Interest?
A · It doubles
Simple Interest is directly proportional to the principal, so doubling principal doubles the interest.
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If the rate of interest is doubled and time is halved, how does the Simple Interest change, assuming principal remains the same?
A · Remains the same
SI \( \propto R \times T \). Doubling R and halving T results in no change in SI.
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A sum of money amounts to \( \$1320 \) in 2 years and \( \$1380 \) in 3 years at simple interest. What is the principal?
A · \( \$1200 \)
Interest for 1 year = 1380 - 1320 = \( \$60 \).Interest for 2 years = 60 \times 2 = \$120.Principal = Amount - Interest = 1320 - 120 = \( \$1200 \).
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If Simple Interest earned on \( \$5000 \) at 4% per annum for 3 years is \( \$600 \), what is the rate of interest?
A · 4%
SI = \( \frac{P \times R \times T}{100} \Rightarrow 600 = \frac{5000 \times R \times 3}{100} \Rightarrow 600 = 150R \Rightarrow R = 4% \). So correct answer is 4%, option A.
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Find the principal if the Simple Interest is \( \$450 \) at 9% per annum for 5 years.
A · \( \$1000 \)
SI = \( \frac{P \times R \times T}{100} \Rightarrow 450 = \frac{P \times 9 \times 5}{100} = 0.45P \Rightarrow P = 1000 \).
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A sum of money is lent at 6% simple interest. If the interest earned in 4 years is \( \$480 \), what is the principal?
A · \( \$2000 \)
SI = \( \frac{P \times R \times T}{100} \Rightarrow 480 = \frac{P \times 6 \times 4}{100} = 0.24P \Rightarrow P = 2000 \).
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If \( \$1500 \) is invested at simple interest and the amount after 3 years is \( \$1800 \), what is the rate of interest per annum?
A · 6.67%
SI = 1800 - 1500 = 300.SI = \( \frac{P \times R \times T}{100} \Rightarrow 300 = \frac{1500 \times R \times 3}{100} = 45R \Rightarrow R = \frac{300}{45} = 6.67\% \).
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A person borrows \( \$5000 \) at simple interest for 2 years and pays back \( \$5600 \). What is the rate of interest?
A · 6%
SI = 5600 - 5000 = 600.SI = \( \frac{P \times R \times T}{100} \Rightarrow 600 = \frac{5000 \times R \times 2}{100} = 100R \Rightarrow R = 6\% \).
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A sum of money is invested at 8% simple interest. If the interest earned in 3 years is \( \$720 \), what is the principal amount?
A · \( \$3000 \)
SI = \( \frac{P \times 8 \times 3}{100} = 0.24P = 720 \Rightarrow P = 3000 \).
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A man borrows \( \$4000 \) at 5% simple interest for 3 years. How much interest will he pay?
A · \( \$600 \)
SI = \( \frac{4000 \times 5 \times 3}{100} = 600 \).
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A person deposits \( \$2500 \) in a bank at 4% simple interest per annum. How much interest will he earn in 1 year and 6 months?
A · \( \$150 \)
Time = 1.5 years.SI = \( \frac{2500 \times 4 \times 1.5}{100} = 150 \).
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A loan of \( \$8000 \) is taken at 6% simple interest for 2 years. What is the total amount to be repaid?
A · \( \$8960 \)
SI = \( \frac{8000 \times 6 \times 2}{100} = 960 \).Total amount = 8000 + 960 = 8960.
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Which of the following statements is true about Simple Interest (SI) and Compound Interest (CI)?
A · SI is calculated only on principal, CI on principal plus interest
Simple Interest is calculated on the principal only, whereas Compound Interest is calculated on principal plus accumulated interest.
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Which of the following is NOT a characteristic of Simple Interest?
B · Interest is added to principal to calculate next period's interest
In Simple Interest, interest is not added to principal for further interest calculation; this is a feature of Compound Interest.
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If \( \$1000 \) is invested at 5% simple interest and \( \$1000 \) at 5% compound interest for 2 years, which will yield more interest?
A · Compound Interest
Compound Interest yields more because interest is calculated on principal plus interest.
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Convert 9 months into years for use in Simple Interest calculations.
A · 0.75 years
9 months = \( \frac{9}{12} = 0.75 \) years.
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A sum is lent for 45 days at 12% per annum simple interest. What fraction of a year is used for the time period?
A · \( \frac{45}{365} \)
Time in years = \( \frac{45}{365} \) assuming a 365-day year.
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Calculate the Simple Interest on \( \$1200 \) at 10% per annum for 8 months.
A · \( \$80 \)
Time = \( \frac{8}{12} = \frac{2}{3} \) years.SI = \( \frac{1200 \times 10 \times \frac{2}{3}}{100} = 80 \). Option A is correct.
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A sum of money is invested for 1 year 9 months at 7% simple interest. What is the time in years used for calculation?
A · 1.75 years
1 year 9 months = 1 + \( \frac{9}{12} = 1.75 \) years.
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A principal of \( \$5000 \) at 5% simple interest amounts to \( \$5750 \). What is the time period in years?
A · 3 years
SI = 5750 - 5000 = 750.SI = \( \frac{5000 \times 5 \times T}{100} = 250T \Rightarrow 750 = 250T \Rightarrow T = 3 \) years.
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If the Simple Interest on a sum for 2 years at 6% is \( \$240 \), what is the total amount after 2 years?
A · \( \$2240 \)
SI = 240 for 2 years at 6%.Principal = \( \frac{240 \times 100}{6 \times 2} = 2000 \).Total amount = Principal + SI = 2000 + 240 = 2240. Option A is correct.
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A sum of money lent at simple interest amounts to \( \$1540 \) in 2 years and to \( \$1815 \) in 3 years. What is the interest for 1 year?
A · \( \$275 \)
Interest for 1 year = 1815 - 1540 = \( \$275 \).
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A sum of money is invested at 8% simple interest per annum. If the total amount after 5 years is \( \$5400 \) and the interest earned is \( \$1600 \), what is the principal?
B · \( \$4000 \)
Principal = Amount - Interest = 5400 - 1600 = \( \$4000 \).
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A loan of \( \$6000 \) is taken at 10% simple interest. If the interest paid is \( \$900 \), what is the time period in years?
A · 1.5 years
SI = \( \frac{6000 \times 10 \times T}{100} = 600T \).Given SI = 900, so 900 = 600T \Rightarrow T = 1.5 \) years.
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A sum of money is invested at simple interest. After 3 years, the interest earned is \( \$360 \). If the rate of interest is 6% per annum, what is the principal?
A · \( \$2000 \)
SI = \( \frac{P \times 6 \times 3}{100} = 0.18P = 360 \Rightarrow P = 2000 \).
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A man borrows \( \$8000 \) at 7.5% simple interest per annum. How much interest will he have to pay after 4 years?
A · \( \$2400 \)
SI = \( \frac{8000 \times 7.5 \times 4}{100} = 2400 \).
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A sum lent at simple interest amounts to \( \$1100 \) in 2 years and \( \$1155 \) in 3 years. What is the rate of interest?
D · 5%
Interest for 1 year = 1155 - 1100 = 55.Principal = 1100 - (55 \times 2) = 1100 - 110 = 990.Rate = \( \frac{SI \times 100}{P \times T} = \frac{55 \times 100}{990 \times 1} = 5.56\% \) approx 5%.
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A sum of money is invested at simple interest. After 5 years, the amount is \( \$1500 \). If the principal was \( \$1200 \), what is the rate of interest per annum?
A · 5%
SI = 1500 - 1200 = 300.Rate = \( \frac{SI \times 100}{P \times T} = \frac{300 \times 100}{1200 \times 5} = 5% \). Option A is correct.
