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Percentage Investment in First Part

CAT 2022 Slot 1 · Quantitative Ability · Easy · Simple Interest

This is an easy Quantitative Ability question from the CAT 2022 Slot 1 paper. It tests Simple Interest. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Alex invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is

  1. A.

    62.5%

  2. B.

    37.5%

  3. C.

    60%

  4. D.

    40%

Answer

B

Explanation

Let the two parts of savings be P1P_1 and P2P_2. Simple interest on first part =P1×15%×4=0.60P1= P_1 \times 15\% \times 4 = 0.60 P_1. Simple interest on second part =P2×12%×3=0.36P2= P_2 \times 12\% \times 3 = 0.36 P_2.

Given 0.60P1=0.36P2  ⟹  P1P2=0.360.60=350.60 P_1 = 0.36 P_2 \implies \frac{P_1}{P_2} = \frac{0.36}{0.60} = \frac{3}{5}.

Percentage of savings in first part =P1P1+P2×100=33+5×100=37.5%= \frac{P_1}{P_1 + P_2} \times 100 = \frac{3}{3 + 5} \times 100 = 37.5\%.

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