CAT 2019

Slot 1

QA

Question & Solution

1. Concept Used

• Topic: Percentage — Chain Comparison of Incomes
• Formula: $$\text{Percentage Excess} = \frac{\text{Kamala's New Income} - \text{Bimala's New Income}}{\text{Bimala's New Income}} \times 100$$

2. Calculation

Let Bimala's income be $100a$. Since Amala's income is 20% more than Bimala's, Amala's income $= 100a \times \frac{120}{100} = 120a$.

Since Amala's income is 20% less than Kamala's, it means Amala's income is 80% of Kamala's income. Therefore, Kamala's income $= 120a \times \frac{100}{80} = 150a$.

Now applying the changes — Kamala's income decreases by 4%: $$\text{New Kamala Income} = 150a \times \left(1 - \frac{4}{100}\right) = 150a \times \frac{96}{100} = 144a$$

Bimala's income increases by 10%: $$\text{New Bimala Income} = 100a \times \left(1 + \frac{10}{100}\right) = 100a \times \frac{110}{100} = 110a$$

Now calculating the percentage by which Kamala's income exceeds Bimala's: $$\text{Percentage Excess} = \frac{144a - 110a}{110a} \times 100 = \frac{34a}{110a} \times 100 = \frac{3400}{110} \approx 30.9% \approx 31%$$

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3. Solution

Answer = Option A (31) ✅

The final calculated value is 31%. After the adjustments, Kamala's income of $144a$ exceeds Bimala's income of $110a$ by approximately 31%.