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Relative Income Percentage Changes

CAT 2019 Slot 1 · Quantitative Ability · Medium · Percentages

This is a medium Quantitative Ability question from the CAT 2019 Slot 1 paper. It tests Percentages. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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

  1. A.

    28

  2. B.

    29

  3. C.

    31

  4. D.

    32

Answer

C

Explanation

Let Amala's income A=120A = 120. A=1.2B  ⟹  B=100A = 1.2 B \implies B = 100. A=0.8K  ⟹  K=150A = 0.8 K \implies K = 150. New Kamala income =150×0.96=144= 150 \times 0.96 = 144. New Bimala income =100×1.10=110= 100 \times 1.10 = 110. Percentage excess =144−110110×100=34110×100=30.9%≈31%= \frac{144 - 110}{110} \times 100 = \frac{34}{110} \times 100 = 30.9\% \approx 31\%.

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