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MathematicsPrevious Year Paper 2024

If A's salary is 31 % more than that of B, then how much percent is B's salary less than that of A (correct to 2 decimal places)?

23.66%

21.53%

27.46%

21.74%

Correct Answer

📐 MA • Math Direct FormulaMathematicsPrevious Year Paper 2024

Option A

23.66%

Quick Summary:

Use the percentage reduction formula $\frac{R}{100+R} \times 100\%$ . Here, $\frac{31}{131} \times 100\% \approx \frac{3100}{131} \approx 23.66\%$ .

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📐MAMath SolutionDirect Formula

📋 Given

A's salary is 31% more than B's salary.

🔢 Formula Used

Percentage Less=(R100+R)×100%\text{Percentage Less} = \left( \frac{R}{100 + R} \right) \times 100\%Percentage Less=(100+RR​)×100%

⚡ Exam Hall Shortcut / Speed Trick

Use the percentage reduction formula $\frac{R}{100+R} \times 100\%$ . Here, $\frac{31}{131} \times 100\% \approx \frac{3100}{131} \approx 23.66\%$ .

⚠️ Common Student Trap / Pitfall

Students often calculate $31\%$ of A's salary directly or use $100$ in the denominator instead of $(100 + 31)$ , leading to the incorrect formula $\frac{31}{100} \times 100\% = 31\%$ .

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Assume B's Salary

Let the salary of B be $100$ . Since A's salary is $31\%$ more than B's salary, we calculate A's salary accordingly.

Salary of B=100\text{Salary of B} = 100Salary of B=100

Calculate A's Salary

A's salary is $100 + 31\% \text{ of } 100 = 100 + 31 = 131$ .

Salary of A=131\text{Salary of A} = 131Salary of A=131

Determine Difference in Salaries

Find how much less B's salary is compared to A's salary.

Difference=131−100=31\text{Difference} = 131 - 100 = 31Difference=131−100=31

Calculate Percentage Difference

Calculate the percentage by which B's salary is less than A's salary with respect to A's salary.

Percentage Less=(31131)×100%≈23.66%\text{Percentage Less} = \left( \frac{31}{131} \right) \times 100\% \approx 23.66\%Percentage Less=(13131​)×100%≈23.66%

✅

A is correct because B's salary is $23.66\%$ less than A's salary.

Core Concepts Used

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Percentage Comparison Base Value Selection Relative Change Formula

💡 EXAM TIP

Whenever given 'A is $R\%$ more than B', the base for finding how much B is less than A changes to $(100 + R)$ . This fundamental base-change logic is also applied in Profit & Loss and Successive Percentage Change problems.

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