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Percentage Rent Share Change

CAT 2024 Slot 1 · Quantitative Ability · Easy · Percentages

This is an easy Quantitative Ability question from the CAT 2024 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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In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 : 6 : 5. They rent a house together, and Kamal pays 15%, Amal pays 12% and Vimal pays 18% of their respective incomes to cover the total house rent in that month. In October, the house rent remains unchanged while their incomes increase by 10%, 12% and 15%, respectively. In October, the percentage of their total income that will be paid as house rent, is nearest to

  1. A.

    14.84

  2. B.

    12.75

  3. C.

    13.26

  4. D.

    15.18

Answer

C

Explanation

Let September incomes be K=800,A=600,V=500K = 800, A = 600, V = 500. Total September income = 19001900. Total rent paid = 15%(800)+12%(600)+18%(500)=120+72+90=28215\%(800) + 12\%(600) + 18\%(500) = 120 + 72 + 90 = 282.

In October:

  • K=800×1.10=880K = 800 \times 1.10 = 880
  • A=600×1.12=672A = 600 \times 1.12 = 672
  • V=500×1.15=575V = 500 \times 1.15 = 575 Total October income = 880+672+575=2127880 + 672 + 575 = 2127.

Percentage of income paid as rent = 2822127×100%≈13.258%≈13.26%\frac{282}{2127} \times 100\% \approx 13.258\% \approx 13.26\%.

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