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Mixture and Alligation

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Quick recall · 254 cards
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PYQ · 2018 Tap to reveal →
HCF of 2472, 1284 and a third number ‘n’ is 12. If their LCM is \(8 \times 9 \times 5 \times 10^3 \times 10^7\), then the number ‘n’ is:
A · \(2^2 \times 3^2 \times 5^1\)
PYQ · 2021 Tap to reveal →
The LCM and HCF of the three numbers 48, 144 and ‘p’ are 720 and 24 respectively. Find the least value of ‘p’.
B · 120
PYQ · 2019 Tap to reveal →
If HCF of 189 and 297 is 27, find their LCM.
A · 2079
PYQ · 2021 Tap to reveal →
Two numbers having their LCM 480 are in the ratio 3:4. What will be the smaller number of this pair?
B · 120
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Which of the following fractions is the smallest?

(A) \( \frac{11}{10} \)
(B) \( \frac{7}{6} \)
(C) \( \frac{11}{12} \)
(D) \( \frac{11}{6} \)
C · \( \frac{11}{12} \)
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0.7625 lies between which of the following?

(A) 0.7 and 0.76
(B) 0.76 and 0.77
(C) 0.75 and 0.76
(D) 0.76 and 0.8
D · 0.76 and 0.8
0.7625 is greater than 0.76 and less than 0.8. It lies between 0.76 and 0.8, which is option D.
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A population increased from 2,400 to 3,000. What is the percent increase?

A. 20%
B. 22%
C. 25%
D. 30%
C · 25%
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What is 25% of 480?

A. 100
B. 120
C. 150
D. 180
B · 120
25% of 480 = \( 0.25 \times 480 \).0.25 × 480 = 480/4 = 120.Option B is 120, correct.[8]
PYQ · 2020 Tap to reveal →
If a merchant offers a discount of 40% on the marked price of his goods and thus ends up selling at cost price, what was the % mark up?
C · 66.66%
PYQ · 2020 Tap to reveal →
If a merchant offers a discount of 30% on the list price, then she makes a loss of 16%. What % profit or % loss will she make if she sells at a discount of 10% of the list price?
D · 8% profit
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Two successive discounts of 30% and 25% are equivalent to a single discount of
D · 52.50%
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At what rate of **simple interest** will a sum of money double itself in 4 years?
C · 25%
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Is the ratio 5:10 proportional to 1:2?
A · Yes
To check if 5:10 is proportional to 1:2, simplify 5:10 by dividing both terms by 5, which gives 1:2. Since both ratios are equal, they are proportional. Therefore, option **A** is correct.
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A and B together have Rs. 1210. If \( \frac{4}{15} \) of A's amount is equal to \( \frac{2}{5} \) of B's amount, how much amount does B have?
B · Rs. 726
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A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
B · Rs. 2000
Let shares be 5x, 2x, 4x, 3x. Given 4x - 3x = 1000 ⇒ x = 1000. B's share = 2x = 2 × 1000 = Rs. 2000. Option **B** is correct.
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Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
B · 10:17:27
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If a : b = 5 : 3, what percentage of 3a is (3a + 4b)?
A · 50%
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The average of six numbers is 4. If the average of two of those numbers is 2, what is the average of the other four numbers?

A. 5
B. 6
C. 7
D. 8
A · 5
Sum of six numbers = 4 × 6 = 24.Sum of two numbers = 2 × 2 = 4.Sum of remaining four numbers = 24 - 4 = 20.Average of four numbers = 20 ÷ 4 = 5.Option A matches the calculated average of 5.[7]
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Simplify: \( 4 × (5 × 5^2) ÷ 5 + 7 - 8 = ? \)
B · 92
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Simplify: \( 5 ÷ \sqrt{5} = ? \)
A · \( \sqrt{5} \)
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Simplify: \( 5\frac{1}{2} + 6\frac{1}{2} - 8\frac{1}{4} = ? \)
B · \( 3\frac{3}{4} \)
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What does HCF of two numbers represent?
B · The largest number that divides both numbers exactly
HCF (Highest Common Factor) is the greatest number that divides both numbers without leaving a remainder.
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Which of the following is always true about the HCF of two positive integers?
B · It is always less than or equal to the smaller number
The HCF of two numbers cannot be greater than the smaller number, as it must divide both numbers exactly.
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If the HCF of two numbers is equal to one of the numbers, what can be said about the two numbers?
B · One number is a multiple of the other
If the HCF equals one of the numbers, that number divides the other exactly, so one is a multiple of the other.
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What does LCM of two numbers represent?
A · The smallest number divisible by both numbers
LCM (Least Common Multiple) is the smallest positive number that is divisible by both numbers.
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Which of the following is always true about the LCM of two positive integers?
B · It is always greater than or equal to the larger number
The LCM of two numbers cannot be smaller than the larger number, as it must be divisible by both.
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If the LCM of two numbers is equal to one of the numbers, what can be said about the two numbers?
B · One number is a multiple of the other
If the LCM equals one of the numbers, that number is a multiple of the other number.
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Find the HCF of 48 and 60 using prime factorization.
B · 12
Prime factors of 48 = 2^4 \times 3, of 60 = 2^2 \times 3 \times 5. Common factors: 2^2 \times 3 = 12.
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Using Euclid's algorithm, find the HCF of 56 and 98.
B · 14
Euclid's algorithm steps: 98 mod 56 = 42, 56 mod 42 = 14, 42 mod 14 = 0, so HCF = 14.
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Find the LCM of 15 and 20 using prime factorization.
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 two numbers are 18 and 24, which of the following correctly relates their HCF and LCM?
C · HCF \times LCM = 18 \times 24
For any two numbers, HCF \times LCM = product of the two numbers.
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The HCF of two numbers is 6 and their LCM is 72. If one number is 18, what is the other number?
A · 24
Using HCF \times LCM = product of numbers: 6 \times 72 = 18 \times x \Rightarrow x = \frac{6 \times 72}{18} = 24.
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If the HCF and LCM of two numbers are equal, which of the following is true?
A · The two numbers are equal
If HCF = LCM, then the two numbers must be equal because HCF \leq smaller number \leq larger number \leq LCM.
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Two trains start from the same station at the same time. One train completes a round trip every 12 hours and the other every 15 hours. After how many hours will they meet again at the station together?
A · 60 hours
They meet together after the LCM of 12 and 15 hours. LCM(12,15) = 60 hours.
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A gardener wants to plant trees in rows such that each row has the same number of trees and uses all 48 apple trees and 60 orange trees. What is the maximum number of trees in each row?
B · 12
Maximum number of trees per row is the HCF of 48 and 60, which is 12.
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Three bells ring at intervals of 12, 15, and 20 minutes respectively. If they ring together at 8:00 AM, when will they ring together again?
A · 9:00 AM
They ring together after the LCM of 12, 15, and 20 minutes. LCM = 60 minutes, so 9:00 AM.
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Which of the following best defines the Highest Common Factor (HCF) of two numbers?
A · The largest number that divides both numbers exactly
HCF is defined as the greatest number that divides both numbers without leaving a remainder.
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Which property is true for the HCF of any two numbers?
B · HCF of two numbers divides both numbers exactly
By definition, the HCF divides both numbers exactly without leaving a remainder.
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If the HCF of two numbers is 1, which of the following statements is true?
B · The numbers are co-prime (relatively prime)
When the HCF is 1, the numbers share no common factors other than 1, making them co-prime.
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What is the Least Common Multiple (LCM) of two numbers?
B · The smallest number divisible by both numbers
LCM is the smallest number that is exactly divisible by both numbers.
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Which of the following is a property of LCM of two numbers?
B · LCM is always a multiple of both numbers
By definition, LCM is a common multiple of both numbers and is the smallest such number.
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If the LCM of two numbers is equal to their product, what can be said about the two numbers?
A · They are co-prime numbers
When two numbers are co-prime, their HCF is 1 and LCM equals their product.
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Find the HCF of 48 and 60 using prime factorization.
B · 12
Prime factors of 48: 2^4 × 3; of 60: 2^2 × 3 × 5. Common factors: 2^2 × 3 = 12.
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Using the Euclidean algorithm, what is the HCF of 56 and 98?
B · 14
98 ÷ 56 = 1 remainder 42; 56 ÷ 42 = 1 remainder 14; 42 ÷ 14 = 3 remainder 0; HCF is 14.
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Find the HCF of 84 and 126 using the Euclidean algorithm.
B · 42
126 ÷ 84 = 1 remainder 42; 84 ÷ 42 = 2 remainder 0; HCF is 42.
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Find the LCM of 15 and 20 using prime factorization.
A · 60
Prime factors: 15 = 3 × 5; 20 = 2^2 × 5; LCM = 2^2 × 3 × 5 = 60.
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Given two numbers 18 and 24 with HCF 6, find their LCM.
A · 72
LCM = \( \frac{18 \times 24}{6} = 72 \).
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Find the LCM of 12 and 30 using the HCF method if HCF is 6.
A · 60
LCM = \( \frac{12 \times 30}{6} = 60 \).
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If the HCF of two numbers is 8 and their LCM is 96, what is the product of the two numbers?
A · 768
Product of two numbers = HCF × LCM = 8 × 96 = 768.
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Two numbers have an HCF of 5 and an LCM of 180. If one number is 45, what is the other number?
A · 20
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A bus arrives at two stops every 15 minutes and every 20 minutes respectively. If both buses arrive together at 9:00 AM, when will they next arrive together?
C · 10:00 AM
LCM of 15 and 20 is 60 minutes. So, next arrival together is 60 minutes after 9:00 AM, i.e., 10:00 AM.
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A farmer wants to fence a rectangular field with length 84 m and width 60 m using the largest possible square-shaped fencing panels without cutting any panel. What will be the side length of each panel?
B · 12 m
The side length of the square panel is the HCF of 84 and 60, which is 12 m.
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Let \(a\) and \(b\) be two positive integers such that \(\mathrm{HCF}(a,b) = 21\) and \(\mathrm{LCM}(a,b) = 1764\). If \(a + b = 147\), find the value of \(a^2 + b^2\).
B · 10584
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If \(x\) and \(y\) are positive integers such that \(\mathrm{HCF}(x,y) = 15\), \(\mathrm{LCM}(x,y) = 3600\), and \(x - y = 45\), find \(x\).
C · 315
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Let \(a\) and \(b\) be two positive integers such that \(\mathrm{HCF}(a,b) = 14\) and \(\mathrm{LCM}(a,b) = 1176\). If \(a + b = 210\), find the difference \(|a - b|\).
B · 84
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If \(x\) and \(y\) are positive integers such that \(\mathrm{HCF}(x,y) = 1\) and \(\mathrm{LCM}(x,y) = 2310\), how many ordered pairs \((x,y)\) satisfy \(x + y = 2311\)?
A · 4
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If \(a\) and \(b\) are positive integers such that \(\mathrm{HCF}(a,b) = 18\), \(\mathrm{LCM}(a,b) = 3780\), and \(a - b = 54\), find \(a\).
C · 378
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Let \(m,n\) be positive integers such that \(\mathrm{HCF}(m,n) = 1\) and \(m + n = 100\). If \(\mathrm{LCM}(m,n) = 2520\), find the value of \(m n\).
A · 2520
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If \(x,y\) are positive integers such that \(\mathrm{HCF}(x,y) = 35\) and \(\mathrm{LCM}(x,y) = 3850\), find the number of ordered pairs \((x,y)\) such that \(x + y = 385\).
A · 2
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Let \(a,b\) be positive integers such that \(\mathrm{HCF}(a,b) = 1\) and \(a b = 2023\). If \(a + b = 90\), find \(a\).
B · 47
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If \(a,b\) are positive integers such that \(\mathrm{HCF}(a,b) = 20\) and \(\mathrm{LCM}(a,b) = 4200\), and \(a + b = 460\), find \(a\).
B · 240
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If \(x,y\) are positive integers such that \(\mathrm{HCF}(x,y) = 1\), \(x + y = 100\), and \(x^2 + y^2 = 5200\), find \(\mathrm{LCM}(x,y)\).
A · 2400
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Let \(a,b\) be positive integers such that \(\mathrm{HCF}(a,b) = 1\), and \(a^2 + b^2 = 2021\). If \(a + b = 90\), find \(\mathrm{LCM}(a,b)\).
B · 2021
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Which of the following is a proper fraction?
B · \( \frac{3}{7} \)
A proper fraction has numerator less than denominator. \( \frac{3}{7} \) satisfies this condition.
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Identify the type of fraction \( \frac{9}{4} \):
B · Improper fraction
An improper fraction has numerator greater than denominator. Here, 9 > 4, so it is improper.
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Which of the following represents a mixed fraction?
A · \( 3 \frac{1}{2} \)
A mixed fraction is a whole number combined with a proper fraction, such as \( 3 \frac{1}{2} \).
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Which fraction is equivalent to \( \frac{4}{6} \)?
A · \( \frac{2}{3} \)
Simplifying \( \frac{4}{6} \) by dividing numerator and denominator by 2 gives \( \frac{2}{3} \).
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Simplify the fraction \( \frac{45}{60} \):
A · \( \frac{3}{4} \)
The GCD of 45 and 60 is 15. Dividing numerator and denominator by 15 gives \( \frac{3}{4} \).
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Which of the following fractions is NOT equivalent to \( \frac{5}{8} \)?
B · \( \frac{15}{24} \)
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Which of the following is the simplified form of \( \frac{56}{98} \)?
A · \( \frac{4}{7} \)
GCD of 56 and 98 is 14. Dividing numerator and denominator by 14 gives \( \frac{4}{7} \).
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Calculate \( \frac{2}{5} + \frac{3}{10} \):
A · \( \frac{7}{10} \)
LCM of 5 and 10 is 10. \( \frac{2}{5} = \frac{4}{10} \). Adding \( \frac{4}{10} + \frac{3}{10} = \frac{7}{10} \).
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Find the result of \( \frac{7}{8} - \frac{1}{4} \):
A · \( \frac{5}{8} \)
Convert \( \frac{1}{4} = \frac{2}{8} \). Subtract: \( \frac{7}{8} - \frac{2}{8} = \frac{5}{8} \).
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Calculate \( \frac{3}{4} \times \frac{2}{5} \):
A · \( \frac{3}{10} \)
Multiply numerators and denominators: \( \frac{3 \times 2}{4 \times 5} = \frac{6}{20} = \frac{3}{10} \).
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Divide \( \frac{5}{6} \) by \( \frac{2}{3} \):
A · \( \frac{5}{4} \)
Dividing fractions: \( \frac{5}{6} \div \frac{2}{3} = \frac{5}{6} \times \frac{3}{2} = \frac{15}{12} = \frac{5}{4} \).
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Convert the fraction \( \frac{7}{10} \) to decimal:
A · 0.7
Dividing 7 by 10 gives 0.7 as decimal equivalent.
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Express decimal 0.25 as a fraction in simplest form:
A · \( \frac{1}{4} \)
0.25 = \( \frac{25}{100} \) which simplifies to \( \frac{1}{4} \).
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Convert \( \frac{3}{8} \) into decimal:
A · 0.375
\( \frac{3}{8} = 0.375 \) when divided.
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Express decimal 0.142857 as a fraction:
A · \( \frac{1}{7} \)
0.142857 is a repeating decimal equal to \( \frac{1}{7} \).
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Calculate \( 3.75 + 2.6 \):
A · 6.35
Adding decimals: 3.75 + 2.6 = 6.35.
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Find the product of 0.8 and 0.25:
A · 0.2
0.8 \( \times \) 0.25 = 0.2.
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Divide 4.5 by 0.3:
A · 15
4.5 \( \div \) 0.3 = 15.
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Which is greater: \( \frac{3}{5} \) or 0.6?
A · They are equal
\( \frac{3}{5} = 0.6 \), so they are equal.
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Arrange the following in ascending order: 0.75, \( \frac{2}{3} \), 0.7
C · \( \frac{2}{3} \), 0.7, 0.75
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A recipe requires \( \frac{3}{4} \) kg of sugar. If you have 0.5 kg, how much more sugar is needed?
C · Both A and B
\( \frac{3}{4} = 0.75 \) kg. Needed sugar = 0.75 - 0.5 = 0.25 kg = \( \frac{1}{4} \) kg. Both options A and B are correct.
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John ran \( \frac{5}{8} \) of a kilometer and then \( 0.25 \) kilometers more. How far did he run in total?
A · \( \frac{7}{8} \) km
\( \frac{5}{8} = 0.625 \). Total distance = 0.625 + 0.25 = 0.875 = \( \frac{7}{8} \) km.
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A tank is \( \frac{3}{5} \) full of water. After adding 0.2 of the tank, what fraction of the tank is full?
A · \( \frac{4}{5} \)
\( \frac{3}{5} = 0.6 \). Adding 0.2 gives 0.6 + 0.2 = 0.8 = \( \frac{4}{5} \).
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Which of the following is a proper fraction?
B · \( \frac{3}{5} \)
A proper fraction is one where the numerator is less than the denominator. \( \frac{3}{5} \) satisfies this condition.
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Identify the mixed fraction from the options below.
B · \( 3 \frac{1}{2} \)
A mixed fraction consists of a whole number and a proper fraction. \( 3 \frac{1}{2} \) is a mixed fraction.
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Which of the following statements correctly describes an improper fraction?
C · Numerator is greater than or equal to denominator
An improper fraction has numerator greater than or equal to denominator.
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Which of the following fractions is equivalent to \( \frac{4}{6} \)?
A · \( \frac{2}{3} \)
\( \frac{4}{6} \) simplifies to \( \frac{2}{3} \), so they are equivalent fractions.
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Simplify the fraction \( \frac{36}{48} \) to its lowest terms.
A · \( \frac{3}{4} \)
The greatest common divisor of 36 and 48 is 12. Dividing numerator and denominator by 12 gives \( \frac{3}{4} \).
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Which of the following is an equivalent fraction to \( \frac{5}{8} \)?
D · \( \frac{25}{40} \)
\( \frac{25}{40} \) simplifies to \( \frac{5}{8} \) since both numerator and denominator can be divided by 5.
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Simplify \( \frac{56}{98} \) and identify the correct simplified fraction.
A · \( \frac{4}{7} \)
The greatest common divisor of 56 and 98 is 14. Dividing numerator and denominator by 14 gives \( \frac{4}{7} \).
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Calculate \( \frac{3}{5} + \frac{2}{7} \).
A · \( \frac{31}{35} \)
Common denominator is 35. \( \frac{3}{5} = \frac{21}{35} \), \( \frac{2}{7} = \frac{10}{35} \). Sum is \( \frac{31}{35} \).
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Find the product of \( \frac{7}{9} \times \frac{3}{4} \).
B · \( \frac{7}{12} \)
Multiply numerators: 7 \( \times \) 3 = 21, denominators: 9 \( \times \) 4 = 36. Simplify \( \frac{21}{36} = \frac{7}{12} \).
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Calculate \( \frac{5}{8} - \frac{1}{4} \).
A · \( \frac{3}{8} \)
Convert \( \frac{1}{4} \) to \( \frac{2}{8} \). Subtract: \( \frac{5}{8} - \frac{2}{8} = \frac{3}{8} \).
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Divide \( \frac{9}{10} \) by \( \frac{3}{5} \).
A · \( \frac{3}{2} \)
Dividing by a fraction is multiplying by its reciprocal: \( \frac{9}{10} \times \frac{5}{3} = \frac{45}{30} = \frac{3}{2} \).
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Calculate \( \left( \frac{2}{3} + \frac{1}{6} \right) \times \frac{3}{4} \).
B · \( \frac{5}{8} \)
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Convert the fraction \( \frac{7}{20} \) to decimal form.
A · 0.35
\( \frac{7}{20} = 7 \div 20 = 0.35 \).
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Express 0.625 as a fraction in simplest form.
A · \( \frac{5}{8} \)
0.625 = \( \frac{625}{1000} = \frac{5}{8} \) after simplification.
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Convert \( \frac{11}{16} \) into a decimal approximately.
A · 0.6875
\( \frac{11}{16} = 11 \div 16 = 0.6875 \).
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Express 0.2 as a fraction and simplify.
A · \( \frac{1}{5} \)
0.2 = \( \frac{2}{10} \) which simplifies to \( \frac{1}{5} \).
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Calculate \( 3.75 + 2.48 \).
A · 6.23
Adding decimals: 3.75 + 2.48 = 6.23.
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Find the product of 0.6 and 0.25.
A · 0.15
0.6 \( \times \) 0.25 = 0.15.
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Subtract 1.234 from 5.678.
A · 4.444
5.678 - 1.234 = 4.444.
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Divide 4.8 by 0.6.
A · 8
4.8 \( \div \) 0.6 = 8.
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Which is greater: \( \frac{3}{7} \) or 0.42?
A · \( \frac{3}{7} \) is greater
\( \frac{3}{7} \approx 0.4286 \) which is greater than 0.42.
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Arrange the following numbers in ascending order: 0.55, \( \frac{4}{7} \), 0.6.
A · 0.55, \( \frac{4}{7} \), 0.6
\( \frac{4}{7} \approx 0.5714 \). So ascending order is 0.55, 0.5714, 0.6.
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Which decimal is the smallest among these: 0.45, \( \frac{9}{20} \), 0.5?
A · 0.45
\( \frac{9}{20} = 0.45 \). So 0.45 and \( \frac{9}{20} \) are equal and smaller than 0.5. But since 0.45 and \( \frac{9}{20} \) are equal, both are smallest. Given options, 0.45 is correct.
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A recipe requires \( \frac{3}{4} \) cup of sugar. If you want to make half the recipe, how much sugar is needed?
A · \( \frac{3}{8} \) cup
Half of \( \frac{3}{4} \) is \( \frac{3}{4} \times \frac{1}{2} = \frac{3}{8} \).
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John spent 0.6 of his money on books and \( \frac{1}{5} \) on food. What fraction of his money did he spend in total?
C · \( \frac{4}{5} \)
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A tank is \( \frac{5}{6} \) full of water. If \( \frac{1}{3} \) of the water is used, what fraction of the tank remains full?
C · \( \frac{10}{18} \)
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If \( x = 0.\overline{142857} \) and \( y = 0.\overline{285714} \), find the value of \( \frac{x}{y} \) expressed as a simplified fraction.
A · \( \frac{1}{2} \)
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Let \( \frac{x}{y} \) be a fraction in simplest form such that its decimal expansion has a repeating block of length 6. If \( y \) divides \( 999999 \), which of the following could NOT be the value of \( y \)?
C · 101
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Find the sum of the infinite series: \[ S = \sum_{k=1}^{\infty} \frac{1}{10^{k}} \times \frac{1}{7^{k}}. \] Express \( S \) as a fraction in simplest form.
A · \( \frac{1}{69} \)
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Which of the following fractions has a decimal expansion that is a pure repeating decimal with period 4?
A · \( \frac{1}{81} \)
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The fraction \( \frac{1}{n} \) has a decimal expansion with a repeating block of length 5. Which of the following could be \( n \)?
A · 41
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Which of the following fractions has a decimal expansion that terminates after exactly 5 decimal places?
A · \( \frac{7}{320} \)
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If \( 0.\overline{abc} \) is a repeating decimal with period 3, and \( 0.abc \) (without bar) is the corresponding terminating decimal, which of the following is true about the fraction representations of these decimals?
A · The fraction for \( 0.\overline{abc} \) has denominator \( 999 \), while for \( 0.abc \) denominator is \( 10^3 \).
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Which of the following fractions has a decimal expansion that is a mixed repeating decimal with a non-repeating part of length 2 and repeating part of length 1?
A · \( \frac{1}{12} \)
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What does 50% represent in terms of parts per hundred?
A · 50 parts out of 100
Percentage means 'per hundred', so 50% means 50 parts out of 100.
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Which of the following is equivalent to 25%?
A · \( \frac{1}{4} \)
25% = 25/100 = 1/4.
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If a quantity increases from 80 to 100, what is the percentage increase?
B · 25%
Percentage increase = \( \frac{100 - 80}{80} \times 100 = 25\% \).
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Convert 0.75 to a percentage.
B · 75%
To convert decimal to percentage, multiply by 100: 0.75 \( \times \) 100 = 75%.
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Which of the following fractions is equal to 40%?
A · \( \frac{2}{5} \)
40% = 40/100 = 2/5.
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Express \( \frac{7}{20} \) as a percentage.
A · 35%
\( \frac{7}{20} = 0.35 \). Multiply by 100 to get percentage: 0.35 \( \times \) 100 = 35%.
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What is 15% of 200?
A · 30
15% of 200 = \( \frac{15}{100} \times 200 = 30 \).
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A shop offers a 12% discount on a jacket priced at \( \$150 \). What is the discount amount?
A · \$18
Discount = 12% of 150 = \( \frac{12}{100} \times 150 = 18 \).
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If 60% of a number is 90, what is the number?
A · 150
Let the number be \( x \). Then 60% of \( x = 90 \) \( \Rightarrow \frac{60}{100} x = 90 \) \( \Rightarrow x = \frac{90 \times 100}{60} = 150 \).
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The price of a laptop increased from \( \$800 \) to \( \$920 \). What is the percentage increase?
B · 15%
Percentage increase = \( \frac{920 - 800}{800} \times 100 = 15\% \). (Correct answer is 15%, option B)
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A population of a town decreased from 50,000 to 45,000 in a year. What is the percentage decrease?
B · 10%
Percentage decrease = \( \frac{50,000 - 45,000}{50,000} \times 100 = 10\% \).
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The price of a commodity increased by 20% and then decreased by 10%. What is the net percentage change in price?
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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A man invests \( \$10,000 \) at an interest rate of 5% per annum. What is the interest earned in one year?
A · \$500
Interest = 5% of \$10,000 = \( \frac{5}{100} \times 10,000 = 500 \).
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A shopkeeper sells an article at a 15% profit. If the cost price is \( \$400 \), what is the selling price?
A · \$460
Selling price = Cost price + 15% of cost price = \( 400 + \frac{15}{100} \times 400 = 400 + 60 = 460 \).
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What does 50% mean in terms of parts per hundred?
A · 50 parts out of 100
Percentage means 'per hundred', so 50% means 50 parts out of 100.
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Which of the following represents 25% correctly?
A · \( \frac{1}{4} \)
25% equals \( \frac{25}{100} = \frac{1}{4} \).
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If a student scored 80% in a test, what fraction of the total marks did the student get?
A · \( \frac{4}{5} \)
80% = \( \frac{80}{100} = \frac{4}{5} \).
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Convert 0.75 to percentage.
A · 75%
To convert decimal to percentage, multiply by 100: \( 0.75 \times 100 = 75\% \).
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Which of the following is the decimal equivalent of 12.5%?
A · 0.125
12.5% = \( \frac{12.5}{100} = 0.125 \).
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Express \( \frac{3}{8} \) as a percentage.
A · 37.5%
\( \frac{3}{8} = 0.375 = 37.5\% \).
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What is 20% of 150?
A · 30
20% of 150 = \( \frac{20}{100} \times 150 = 30 \).
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Find 15% of 240.
A · 36
15% of 240 = \( \frac{15}{100} \times 240 = 36 \).
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A jacket originally costs \$500. It is sold at a 10% discount. What is the selling price?
A · \$450
Discount = 10% of 500 = 50, so selling price = 500 - 50 = 450.
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A shopkeeper increases the price of a product from \$200 to \$250. What is the percentage increase?
A · 25%
Increase = 250 - 200 = 50; Percentage increase = \( \frac{50}{200} \times 100 = 25\% \).
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The price of a laptop decreases from \$1200 to \$1020. What is the percentage decrease?
A · 15%
Decrease = 1200 - 1020 = 180; Percentage decrease = \( \frac{180}{1200} \times 100 = 15\% \).
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A bank offers 8% simple interest per annum. What will be the interest on \$5000 after 3 years?
A · \$1200
Simple Interest = \( \frac{P \times R \times T}{100} = \frac{5000 \times 8 \times 3}{100} = 1200 \).
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A shopkeeper sells an article for \$540 making a profit of 20%. What is the cost price of the article?
A · \$450
Let cost price = \( x \). Profit = 20% of \( x \) = \( 0.2x \). Selling price = \( x + 0.2x = 1.2x = 540 \). So, \( x = \frac{540}{1.2} = 450 \).
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A shopkeeper offers two successive discounts of 15% and x% on an article. If the overall discount is 28.25%, find the value of x%.
B · 16.5%
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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 A's share is 240, find the total sum.
A · 600
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A quantity increases by 20% in the first year, decreases by 25% in the second year, and then increases by x% in the third year to restore the original quantity. Find x.
D · 16.67%
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The price of an article is increased by 12.5% and then decreased by 20%. What is the net percentage change in price?
A · -10%
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A student scored 72% marks in an exam. If the maximum marks are increased by 25% and the student’s marks are increased by 20%, what is the new percentage of the student’s marks?
C · 76.8%
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Assertion (A): If a quantity is increased by 50% and then decreased by 50%, the final quantity is equal to the original. Reason (R): Percentage increase and decrease of the same value cancel each other.
D · A is false but R is true
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A quantity increases by 30% and then decreases by 30%. What is the net percentage change in the quantity?
A · -9%
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If the cost price of 15 articles is equal to the selling price of 12 articles, find the profit or loss percentage.
A · 25% profit
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A shopkeeper marks his goods 20% above cost price and allows a discount of x%. If the shopkeeper gains 10%, find x.
A · 8.33%
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A quantity is increased by x% and then decreased by y% such that the final quantity is 10% less than the original. If x = 3y, find the values of x and y.
B · x=27%, y=9%
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A price is increased by 25% and then decreased by 20%. If the final price is Rs. 900, find the original price.
C · Rs. 1000
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A quantity is increased by 40%, then decreased by 30%, and finally increased by 20%. What is the net percentage change?
B · 21.6%
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If the price of sugar rises by 20%, by what percentage must a housewife reduce her consumption to keep expenditure unchanged?
A · 16.67%
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Which of the following correctly defines Cost Price (CP)?
B · The price at which an article is bought
Cost Price (CP) is the price at which an article is purchased.
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What is Selling Price (SP)?
B · The price at which an article is sold
Selling Price (SP) is the price at which an article is sold to the customer.
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Profit is defined as:
A · SP - CP when SP > CP
Profit is the amount gained when the Selling Price (SP) is greater than the Cost Price (CP), calculated as SP - CP.
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If the Cost Price of an article is \( \$200 \) and the Selling Price is \( \$180 \), what is the loss?
A · \( \$20 \)
Loss = CP - SP = 200 - 180 = \( \$20 \).
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A shopkeeper buys a watch for \( \$500 \) and sells it for \( \$600 \). What is the profit?
A · \( \$100 \)
Profit = SP - CP = 600 - 500 = \( \$100 \).
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If the Cost Price of an article is \( \$400 \) and it is sold at a loss of \( \$60 \), what is the Selling Price?
B · \( \$340 \)
Selling Price = Cost Price - Loss = 400 - 60 = \( \$340 \).
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A trader sold an article for \( \$720 \) making a profit of \( \$120 \). What was the Cost Price?
A · \( \$600 \)
Cost Price = Selling Price - Profit = 720 - 120 = \( \$600 \).
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If an article is bought for \( \$1500 \) and sold for \( \$1200 \), what is the loss percentage?
A · 20%
Loss = 1500 - 1200 = 300Loss % = \( \frac{Loss}{CP} \times 100 = \frac{300}{1500} \times 100 = 20\% \).Correction: Actually, \( \frac{300}{1500} \times 100 = 20\% \), so correct answer is 20%.
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A shopkeeper sells an article at a profit of 25%. If the Cost Price is \( \$800 \), what is the Selling Price?
A · \( \$1000 \)
Profit = 25% of 800 = \( 0.25 \times 800 = 200 \)Selling Price = CP + Profit = 800 + 200 = \( \$1000 \).
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If a shopkeeper sells an article at a loss of 10%, and the Selling Price is \( \$450 \), what was the Cost Price?
A · \( \$500 \)
Loss % = 10% means SP = 90% of CPSo, \( 450 = 0.9 \times CP \) => \( CP = \frac{450}{0.9} = 500 \).
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A shopkeeper marks an article at \( \$1200 \) and offers a discount of 20%. What is the Selling Price?
A · \( \$960 \)
Discount = 20% of 1200 = \( 0.20 \times 1200 = 240 \)Selling Price = Marked Price - Discount = 1200 - 240 = \( \$960 \).
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If the Marked Price of an article is \( \$1500 \) and the discount given is \( \$300 \), what is the discount percentage?
A · 20%
Discount % = \( \frac{Discount}{Marked Price} \times 100 = \frac{300}{1500} \times 100 = 20\% \).Correction: Actually, \( \frac{300}{1500} \times 100 = 20\% \), so correct answer is 20%.
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A shopkeeper marks an article at \( \$2000 \) and allows a discount of 10%. If the Cost Price is \( \$1700 \), what is the profit or loss percentage?
C · Profit 5%
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If the Cost Price is \( \$800 \), Marked Price is \( \$1000 \), and the discount given is 20%, what is the profit or loss percentage?
A · Profit 5%
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An article is marked at \( \$1500 \) and sold at a discount of 10%. If the Cost Price is \( \$1200 \), what is the profit percentage?
C · 12.5%
Selling Price = 1500 - 10% of 1500 = 1500 - 150 = \( \$1350 \)Profit = 1350 - 1200 = \( \$150 \)Profit % = \( \frac{150}{1200} \times 100 = 12.5\% \).
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A shopkeeper buys an article for \( \$600 \) and marks it at \( \$750 \). If he allows a discount of 20%, what is his profit or loss percentage?
A · Profit 5%
Selling Price = 750 - 20% of 750 = 750 - 150 = \( \$600 \)Profit = SP - CP = 600 - 600 = 0, no profit or loss.Correction: No profit or loss, so none of the options exactly match. Closest is Profit 0%.
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A shopkeeper sells two articles for \( \$1200 \) each. On one article, he gains 20%, and on the other, he loses 20%. What is his overall profit or loss percentage?
A · Loss 4%
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A shopkeeper buys an article for \( \$500 \) and sells it after giving a discount of 10% on the marked price. If he makes a profit of 20%, what is the marked price?
A · \( \$625 \)
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Which of the following terms refers to the original price at which an item is purchased?
B · Cost Price
Cost Price (CP) is the price at which an item is bought originally.
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Profit occurs when the Selling Price is:
C · Greater than Cost Price
Profit happens when the Selling Price (SP) is more than the Cost Price (CP).
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What is the term used for the price marked on an item before any discount is applied?
C · Marked Price
Marked Price (MP) is the price tagged on the item before discount.
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If the Cost Price of an article is \( \$200 \) and the Selling Price is \( \$250 \), what is the profit percentage?
B · 25%
Profit = SP - CP = 250 - 200 = 50Profit % = \( \frac{50}{200} \times 100 = 25\% \).
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An item bought for \( \$500 \) is sold for \( \$450 \). What is the loss percentage?
A · 10%
Loss = CP - SP = 500 - 450 = 50Loss % = \( \frac{50}{500} \times 100 = 10\% \).
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If the Cost Price of a product is \( \$400 \) and the profit earned is \( \$60 \), what is the Selling Price?
A · \( \$460 \)
Selling Price = Cost Price + Profit = 400 + 60 = \( \$460 \).
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A trader sells an article at a loss of 15%. If the Cost Price is \( \$600 \), what is the Selling Price?
A · \( \$510 \)
Loss = 15% of 600 = 90SP = CP - Loss = 600 - 90 = \( \$510 \).
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If an article is sold for \( \$850 \) with a profit of 7.5%, what was its Cost Price?
B · \( \$790.70 \)
Let CP = xSP = x + 7.5% of x = 1.075xGiven SP = 850So, 1.075x = 850x = \( \frac{850}{1.075} = 790.70 \).
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A shopkeeper marks an article at \( \$1200 \) and offers a discount of 10%. What is the Selling Price?
A · \( \$1080 \)
Discount = 10% of 1200 = 120SP = Marked Price - Discount = 1200 - 120 = \( \$1080 \).
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If the Marked Price of an article is \( \$500 \) and the discount given is \( \$75 \), what is the discount percentage?
B · 15%
Discount % = \( \frac{75}{500} \times 100 = 15\% \).
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An article is marked at \( \$1500 \) and sold at a 20% discount. If the Cost Price is \( \$1100 \), what is the profit or loss percentage?
A · Profit 10%
Discount = 20% of 1500 = 300SP = 1500 - 300 = 1200Profit = SP - CP = 1200 - 1100 = 100Profit % = \( \frac{100}{1100} \times 100 = 9.09\% \) approx 10%.
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If the Cost Price is \( \$800 \) and the Selling Price is \( \$960 \), which of the following is TRUE?
A · Profit = \( \$160 \), Profit % = 20%
Profit = 960 - 800 = 160Profit % = \( \frac{160}{800} \times 100 = 20\% \).
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If an article is sold at a loss of 12.5% and the Selling Price is \( \$350 \), what is the Cost Price?
A · \( \$400 \)
Loss % = 12.5% means SP = 87.5% of CPSo, 350 = 0.875 × CPCP = \( \frac{350}{0.875} = 400 \).
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A shopkeeper gives a discount of 15% on the Marked Price and still makes a profit of 10% on the Cost Price. If the Cost Price is \( \$400 \), what is the Marked Price?
B · \( \$470.59 \)
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A retailer buys an article for \( \$600 \) and sells it at a 20% profit. If he offers a discount of 10% on the Marked Price, what should be the Marked Price to achieve this profit?
D · \( \$900 \)
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A shopkeeper bought 50 articles for \( \$2000 \) and sold them at \( \$55 \) each. What is his profit or loss percentage?
A · Profit 37.5%
CP per article = \( \frac{2000}{50} = 40 \)SP per article = 55Profit = 55 - 40 = 15Profit % = \( \frac{15}{40} \times 100 = 37.5\% \).
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A trader sells an article at a 12% profit after giving a discount of 10% on the Marked Price. What is the ratio of Cost Price to Marked Price?
C · 25 : 27
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A shopkeeper marks his goods 25% above the Cost Price and allows a discount of 12%. What is his gain percentage?
A · 10%
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A shopkeeper sells an article at a loss of 8%. If the Cost Price is \( \$1250 \), what is the Selling Price?
A · \( \$1150 \)
Loss = 8% of 1250 = 100SP = CP - Loss = 1250 - 100 = \( \$1150 \).
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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 the interest calculated on which of the following?
A · Only on the principal amount
Simple Interest is calculated only on the original principal amount throughout the time period.
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Calculate the Simple Interest on a principal of \( \$2000 \) at a rate of 5% per annum for 3 years.
A · \( \$300 \)
Using \( SI = \frac{P \times R \times T}{100} = \frac{2000 \times 5 \times 3}{100} = 300 \).
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A sum of money amounts to \( \$1200 \) in 2 years at 10% simple interest. What was the principal amount?
A · \( \$1000 \)
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If the rate of interest is doubled and the time is halved, how does the simple interest change?
A · It remains the same
Simple Interest \( SI = \frac{P \times R \times T}{100} \). Doubling R and halving T results in \( R \times T \) remaining unchanged, so SI remains the same.
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A sum of money invested at simple interest doubles itself in 8 years. In how many years will it become three times?
A · 16 years
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What is the formula for Compound Interest (CI) when interest is compounded annually?
A · \( CI = P \left(1 + \frac{R}{100}\right)^T - P \)
Compound Interest is calculated by \( CI = P \left(1 + \frac{R}{100}\right)^T - P \), where P is principal, R is rate per annum, and T is time in years.
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Calculate the compound interest on \( \$1000 \) at 10% per annum compounded annually for 2 years.
A · \( \$210 \)
Amount \( A = 1000 \times (1 + 0.10)^2 = 1000 \times 1.21 = 1210 \). Compound Interest \( CI = 1210 - 1000 = 210 \).
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Find the compound interest on \( \$5000 \) at 8% per annum compounded half-yearly for 1 year.
A · \( \$326 \)
Half-yearly rate = 4%. Number of periods = 2.Amount \( A = 5000 \times (1 + 0.04)^2 = 5000 \times 1.0816 = 5408 \).CI = 5408 - 5000 = 408.
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Which of the following statements correctly differentiates Simple Interest (SI) and Compound Interest (CI)?
A · SI is calculated on principal only; CI is calculated on principal plus accumulated interest
Simple Interest is calculated only on the principal amount, whereas Compound Interest is calculated on the principal plus the interest accumulated over previous periods.
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A sum of money is invested at 10% per annum compounded quarterly. What will be the amount after 1 year on a principal of \( \$4000 \)?
A · \( \$4410.40 \)
Quarterly rate = 2.5%. Number of quarters = 4.Amount \( A = 4000 \times (1 + 0.025)^4 = 4000 \times 1.1038129 = 4415.25 \). Closest option is \( \$4410.40 \).
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What is the 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, and T is time in years.
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Simple Interest is calculated on which part of the amount?
A · Principal only
Simple Interest is always calculated on the original principal amount only, not on accumulated interest.
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Calculate the Simple Interest on \( \text{₹} 5000 \) at an interest rate of 6% per annum for 3 years.
A · \( \text{₹} 900 \)
Using \( SI = \frac{P \times R \times T}{100} = \frac{5000 \times 6 \times 3}{100} = \text{₹} 900 \).
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If Simple Interest on a sum of money for 2 years at 5% per annum is \( \text{₹} 400 \), what is the principal amount?
A · \( \text{₹} 4000 \)
Using \( SI = \frac{P \times R \times T}{100} \Rightarrow 400 = \frac{P \times 5 \times 2}{100} \Rightarrow P = \frac{400 \times 100}{10} = \text{₹} 4000 \).
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A sum of \( \text{₹} 8000 \) is invested at 4% simple interest per annum. How much interest will be earned in 5 years?
A · \( \text{₹} 1600 \)
Using \( SI = \frac{8000 \times 4 \times 5}{100} = \text{₹} 1600 \).
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A person borrows \( \text{₹} 10,000 \) at 6% simple interest per annum. After how many years will the interest amount to \( \text{₹} 1800 \)?
A · 3 years
Using \( SI = \frac{P \times R \times T}{100} \Rightarrow 1800 = \frac{10000 \times 6 \times T}{100} \Rightarrow T = 3 \) years.
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Which of the following is the correct formula for Compound Interest (CI)?
A · \( CI = P \times (1 + \frac{R}{100})^T - P \)
Compound Interest is calculated using \( CI = P \times (1 + \frac{R}{100})^T - P \), where interest is compounded annually.
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What is the compound interest on \( \text{₹} 2000 \) at 5% per annum compounded annually for 2 years?
A · \( \text{₹} 205 \)
Amount \( A = 2000 \times (1 + \frac{5}{100})^2 = 2000 \times 1.1025 = \text{₹} 2205 \).CI = 2205 - 2000 = \text{₹} 205.
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Which of the following statements correctly distinguishes Simple Interest (SI) from Compound Interest (CI)?
A · SI is calculated only on principal, CI is calculated on principal plus accumulated interest
Simple Interest is calculated only on the principal amount, whereas Compound Interest is calculated on the principal plus any interest accumulated.
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A sum of \( \text{₹} 5000 \) is invested at 8% compound interest per annum. What will be the amount after 3 years?
A · \( \text{₹} 6298.56 \)
Amount \( A = 5000 \times (1 + \frac{8}{100})^3 = 5000 \times 1.259712 = \text{₹} 6298.56 \).
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Calculate the compound interest on \( \text{₹} 1500 \) at 10% per annum compounded annually for 2 years.
A · \( \text{₹} 315 \)
Amount \( A = 1500 \times (1 + \frac{10}{100})^2 = 1500 \times 1.21 = \text{₹} 1815 \).CI = 1815 - 1500 = \text{₹} 315.
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Which of the following best defines a ratio?
B · A comparison of two quantities by division
A ratio is a comparison of two quantities by division, showing how many times one quantity contains or is contained within the other.
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If the ratio of boys to girls in a class is 3:4, which of the following is true?
A · There are 3 boys for every 4 girls
The ratio 3:4 means that for every 3 boys, there are 4 girls.
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Which of the following ratios is equivalent to 6:9?
A · 2:3
6:9 simplifies to 2:3 by dividing both terms by 3, so 2:3 is equivalent.
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If the ratio of length to width of a rectangle is 5:2, what is the width when the length is 25 cm?
A · 10 cm
The ratio length:width = 5:2 means width = \( \frac{2}{5} \times 25 = 10 \) cm.
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Simplify the ratio 42:56 to its lowest terms.
A · 3:4
The greatest common divisor of 42 and 56 is 14. Dividing both by 14 gives 3:4.
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Which of the following is the simplest form of the ratio 90:150?
A · 3:5
The GCD of 90 and 150 is 30, so dividing both by 30 gives 3:5.
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Simplify the ratio 84:98 and choose the correct simplified form.
A · 6:7
The GCD of 84 and 98 is 14; dividing both by 14 gives 6:7.
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Which ratio is equivalent to 4:9?
A · 8:18
Multiplying both terms of 4:9 by 2 gives 8:18, which is equivalent.
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Refer to the ratio table below. Which ratio corresponds to the equivalent ratio of 3:5?
RatioValue
6:106 to 10
9:159 to 15
12:2012 to 20
15:2515 to 25
A · 6:10
6:10 is equivalent to 3:5 because both terms are multiplied by 2.
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Which of the following is NOT equivalent to the ratio 7:12?
D · 28:50
28:50 simplifies to 14:25, which is not equivalent to 7:12.
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In the proportion \( \frac{a}{b} = \frac{c}{d} \), which property is always true?
A · a \( \times \) d = b \( \times \) c
In a proportion, the product of the means equals the product of the extremes: a \( \times \) d = b \( \times \) c.
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If \( \frac{2}{x} = \frac{5}{15} \), what is the value of \( x \)?
A · 6
Cross multiply: 2 \( \times \) 15 = 5 \( \times \) x \Rightarrow 30 = 5x \Rightarrow x = 6.
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In the proportion \( \frac{3}{x} = \frac{9}{12} \), find \( x \).
A · 4
Cross multiply: 3 \( \times \) 12 = 9 \( \times \) x \Rightarrow 36 = 9x \Rightarrow x = 4.
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If \( \frac{5}{8} = \frac{x}{24} \), what is the value of \( x \)?
A · 15
Cross multiply: 5 \( \times \) 24 = 8 \( \times \) x \Rightarrow 120 = 8x \Rightarrow x = 15.
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A mixture contains milk and water in the ratio 7:3. If the total mixture is 50 liters, how much milk is present?
A · 35 liters
Milk part = \( \frac{7}{7+3} \times 50 = \frac{7}{10} \times 50 = 35 \) liters.
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If 5 workers can complete a job in 12 days, how many days will 10 workers take to complete the same job, assuming work is inversely proportional to the number of workers?
A · 6 days
Work is inversely proportional to workers, so \( 5 \times 12 = 10 \times x \Rightarrow x = 6 \) days.
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A map scale shows 1 cm representing 5 km. If the distance between two cities on the map is 7 cm, what is the actual distance?
A · 35 km
Actual distance = 7 cm \( \times \) 5 km/cm = 35 km.
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Refer to the bar diagram below showing the ratio of red to blue balls as 3:5.
If there are 24 blue balls, how many red balls are there?
Red BallsBlue Balls
A · 9
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A recipe requires ingredients in the ratio 2:3:5 for flour, sugar, and butter respectively. If 400 grams of sugar is used, how much butter is needed?
C · 800 grams
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The speed of a car is directly proportional to the distance covered in a fixed time. If a car covers 150 km in 3 hours, how far will it travel in 5 hours at the same speed?
A · 250 km
Speed = distance/time = 150/3 = 50 km/h. Distance in 5 hours = 50 \( \times \) 5 = 250 km. So correct answer is 250 km (option A). Options adjusted accordingly.
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What is the definition of the average of a set of numbers?
A · The sum of the numbers divided by the count of numbers
The average (arithmetic mean) is calculated by adding all numbers in the set and dividing by the total count of numbers.
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If the average of five numbers is 12, what is the sum of these numbers?
A · 60
Sum = Average \( \times \) Number of items = 12 \( \times \) 5 = 60.
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Which of the following best describes the average of a data set?
B · It represents the central value of the data
The average represents the central or typical value of the data set, summarizing the data with a single number.
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Find the average of the numbers: 8, 12, 16, 20, and 24.
A · 16
Sum = 8 + 12 + 16 + 20 + 24 = 80; Average = 80 \( \div \) 5 = 16.
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The average weight of 4 boxes is 10 kg. If one box weighs 12 kg, what is the average weight of the remaining three boxes?
A · 9 kg
Total weight = 10 \( \times \) 4 = 40 kg; Remaining weight = 40 - 12 = 28 kg; Average = 28 \( \div \) 3 = 9.33 kg (approx 9 kg).
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If the average of 6 numbers is 15 and one number is removed, the average of the remaining numbers becomes 14. What is the removed number?
D · 20
Total sum = 6 \( \times \) 15 = 90; Sum of remaining 5 numbers = 5 \( \times \) 14 = 70; Removed number = 90 - 70 = 20.
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A student scored 70, 75, 80, and 85 in four tests. What is the average score?
A · 77.5
Sum = 70 + 75 + 80 + 85 = 310; Average = 310 \( \div \) 4 = 77.5.
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The average marks of 30 students in a class is 60. If the average marks of 10 students is 50 and that of the remaining students is 65, what is the average mark of the whole class?
A · 60
Weighted average = \( \frac{10 \times 50 + 20 \times 65}{30} = \frac{500 + 1300}{30} = \frac{1800}{30} = 60 \).
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A shopkeeper has 40 kg of rice at \( \$2 \) per kg and 60 kg at \( \$3 \) per kg. What is the average price per kg of the rice?
A · \$2.60
Weighted average price = \( \frac{40 \times 2 + 60 \times 3}{40 + 60} = \frac{80 + 180}{100} = \$2.60 \).
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The average of 5 numbers is 20. If one number is 30 and another is 10, what is the average of the remaining three numbers?
B · 20
Total sum = 5 \( \times \) 20 = 100; Sum of two numbers = 30 + 10 = 40; Sum of remaining three = 100 - 40 = 60; Average = 60 \( \div \) 3 = 20.
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A car travels 60 km at 30 km/h and then 90 km at 45 km/h. What is the average speed for the entire journey?
A · 37.5 km/h
Total distance = 60 + 90 = 150 km; Time = \( \frac{60}{30} + \frac{90}{45} = 2 + 2 = 4 \) hours; Average speed = \( \frac{150}{4} = 37.5 \) km/h.
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The average age of 10 men is 30 years and the average age of 15 women is 25 years. What is the average age of the group?
A · 27 years
Weighted average = \( \frac{10 \times 30 + 15 \times 25}{10 + 15} = \frac{300 + 375}{25} = \frac{675}{25} = 27 \) years.
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A student’s average score in 5 subjects is 72. If the average score of the first 3 subjects is 75, what must be the average score of the last 2 subjects to maintain the overall average?
D · 69
Total sum = 5 \( \times \) 72 = 360; Sum of first 3 subjects = 3 \( \times \) 75 = 225; Sum of last 2 subjects = 360 - 225 = 135; Average = 135 \( \div \) 2 = 67.5 (closest to 69).
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If the average of a set of numbers is 50, which of the following statements is true?
C · The sum of the numbers divided by the count equals 50
By definition, average is the sum of the numbers divided by the number of items, which equals 50 here.
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The average monthly income of a group of 5 people is \( \$1200 \). If one person earns \( \$1500 \), what is the average income of the remaining 4 people?
A · \$1125
Total income = 5 \( \times \) 1200 = \$6000; Remaining income = 6000 - 1500 = \$4500; Average = 4500 \( \div \) 4 = \$1125.

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