Login
OR
Don't worry. We'll fix this for you!
In competitive entrance exams, solving mathematical problems quickly and accurately is crucial. Using formulas effectively helps you achieve both speed and precision. Formulas are like ready-made tools crafted to solve specific types of mathematical problems, saving you from lengthy calculations.
Understanding the variables, units, and what each formula represents is essential before applying them. This section will develop your ability to use formulas across diverse topics such as number operations, fractions, percentages, simple interest, and ratios.
Each concept will build on the previous, with step-by-step examples tailored for easy understanding and practical application, especially in the Indian context but universally applicable.
Basic arithmetic operations-addition, subtraction, multiplication, and division-form the foundation of mathematical problem solving. Formulas help standardize these operations and can be adapted for various problems involving numbers and units.
Let's consider the formulas with examples, using metric units like meters (m), kilograms (kg), and INR currency where applicable.
| Operation | Formula | Variables | Example |
|---|---|---|---|
| Addition | \( S = a + b \) | \(a, b\): numbers or quantities | \(5\,m + 3\,m = 8\,m\) |
| Subtraction | \( D = a - b \) | \(a, b\): numbers or quantities, \(a \geq b\) | \(10\,kg - 4\,kg = 6\,kg\) |
| Multiplication | \( P = a \times b \) | \(a, b\): numbers or quantities | \(7 \times 4 = 28\) |
| Division | \( Q = \frac{a}{b} \) | \(a, b\): numbers or quantities, \(b eq 0\) | \(\frac{20\,\text{INR}}{4} = 5\,\text{INR}\) |
Note: Always ensure that the quantities being added or subtracted have the same units. If units differ (e.g., meters and centimeters), first convert them to the same unit.
Fractions and decimals represent parts of a whole. Being comfortable converting between them allows you to perform operations and comparisons effectively.
The main formula to convert a fraction \(\frac{a}{b}\) into decimal form is:
For example, to convert \(\frac{3}{4}\) into decimal, divide 3 by 4 yielding 0.75.
Operations on fractions-addition, subtraction, multiplication, division-must follow the rules of equivalent denominators or conversion to decimals when appropriate. Comparing fractions is easier once converted to decimals.
Percentages express quantities as parts per hundred, very common in price calculations, growth rates, and discounts. Calculating discounts accurately is critical in financial problems.
The primary formulas used are:
graph TD A[Start with Marked Price] --> B[Calculate Discount = (Discount % x Marked Price) / 100] B --> C[Subtract Discount from Marked Price] C --> D[Get Selling Price]
Simple Interest is the extra money earned or paid on the principal amount over a certain time period at a fixed interest rate. Knowing how to calculate simple interest is important for many money-related problems.
The formula for Simple Interest (SI) is:
Here, the principal \(P\) is multiplied by the rate \(R\) and time \(T\), then divided by 100 to calculate the interest amount.
Ratios compare quantities, while proportions state that two ratios are equal. These formulas help in scaling quantities and solving mixture problems effectively.
Key formula for proportion is:
This formula is pivotal when solving problems such as mixing solutions, dividing quantities, or scaling figures.
Formulas are essential in basic mathematics for faster and accurate problem solving. Understanding each variable, unit consistency, and the underlying concepts help apply formulas confidently across topics.
Step 1: Identify given values:
Step 2: Calculate discount amount using formula:
\[ \text{Discount} = \frac{15 \times 1200}{100} = \frac{18000}{100} = Rs.180 \]
Step 3: Calculate selling price:
\[ \text{Selling Price} = 1200 - 180 = Rs.1020 \]
Answer: The bag will cost Rs.1020 after discount.
Step 1: Note the values:
Step 2: Apply the simple interest formula:
\[ SI = \frac{P \times R \times T}{100} = \frac{10,000 \times 6 \times 3}{100} = \frac{180,000}{100} = Rs.1800 \]
Answer: Simple interest on the loan is Rs.1800.
Step 1: Let the quantity of the first solution be \(3x\), and the second solution \(2x\).
Step 2: Total mixture is given:
\[ 3x + 2x = 25 \]
Step 3: Solve for \(x\):
\[ 5x = 25 \implies x = \frac{25}{5} = 5 \]
Step 4: Calculate quantities:
Answer: 15 liters of first solution and 10 liters of second solution are mixed.
Step 1: Convert \(\frac{3}{4}\):
\[ \frac{3}{4} = 3 \div 4 = 0.75 \]
Step 2: Convert \(\frac{7}{10}\):
\[ \frac{7}{10} = 7 \div 10 = 0.7 \]
Step 3: Compare decimals:
\(0.75 > 0.7\), so \(\frac{3}{4}\) is greater than \(\frac{7}{10}\).
Answer: \(\frac{3}{4}\) is the larger fraction.
Step 1: Calculate the increase:
\[ \text{Increase} = 50 - 40 = Rs.10 \]
Step 2: Apply percentage increase formula:
\[ \% \text{Increase} = \frac{\text{Increase}}{\text{Original Price}} \times 100 = \frac{10}{40} \times 100 = 25\% \]
Answer: The price of sugar increased by 25%.
When to use: When problems involve mixed units to avoid calculation errors.
When to use: When calculating discounts or interest to simplify mental arithmetic.
When to use: When solving proportion equations to find unknown variables.
When to use: To quickly recall simple interest calculation during exams.
When to use: To maintain accuracy in intermediate steps of calculations.
Progress tracking is paywalled — subscribe to mark subtopics as understood and save your streak.
Go to practice →
Your Score
Your Rank
| Rank | Name | Score |
|---|
