The income of Amala is $20 \%$ more than that of Bimala and $20 \%$ less than that of Kamala. If Kamala's income goes down by $4 \%$ and Bimala's goes up by $10 \%$ , then the percentage by which Kamala's income would exceed Bimala's is nearest to

$29$

$28$

$31$

$32$

✅ Correct Option: 3

We need to find how much more Kamala earns compared to Bimala after both their incomes change. We'll work with the relationships given systematically.

We assume Bimala's income = Rs. 100

When dealing with percentage problems, assuming one value as 100 makes calculations much easier. Since we're looking for percentage differences, the actual amounts don't matter - only the ratios between them.

Amala earns 20% more than Bimala

Amala's income = 100 + 20% of 100 = 100 + 20 = Rs. 120

Amala earns 20% less than Kamala

This means: Amala = Kamala - 20% of Kamala = 0.80 × Kamala

So: 120 = 0.80 × Kamala

Therefore: Kamala = 120 ÷ 0.80 = Rs. 150

Quick Check: 20% of 150 = 30, so 150 - 30 = 120

Bimala's income goes up by 10%

New income = 100 + 10% of 100 = 100 + 10 = Rs. 110

Kamala's income goes down by 4%

New income = 150 - 4% of 150 = 150 - 6 = Rs. 144

When we want to find by what percentage A exceeds B:

$\text{Percentage} = \dfrac{\text{A - B}}{\text{B}} \times 100$

$\text{Required percentage} = \dfrac{144 - 110}{110} \times 100$

$= \dfrac{34}{110} \times 100$

$= \dfrac{34}{11} \times 10 = 30.9\%$

Since the question asks for the nearest percentage, 31% is our answer.

When solving percentage comparison problems:

Assume convenient values (like 100) for easier calculation
Work step-by-step through each relationship
Always verify your intermediate results
Use the standard formula for percentage excess: $\dfrac{\text{Difference}}{\text{Base}} \times 100$

Answer: 31%

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The income of Amala is $20 \%$ more than that of Bimala and $20 \%$ less than that of Kamala. If Kamala's income goes down by $4 \%$ and Bimala's goes up by $10 \%$ , then the percentage by which Kamala's income would exceed Bimala's is nearest to