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Simple Interest Reinvestment

CAT 2024 Slot 1 · Quantitative Ability · Easy · Simple Interest

This is an easy Quantitative Ability question from the CAT 2024 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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An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is

  1. A.

    4

  2. B.

    3

  3. C.

    6

  4. D.

    5

Answer

C

Explanation

Let the investment period in Bank A be tt years. Interest from Bank A: IA=10000×0.05×t=500tI_A = 10000 \times 0.05 \times t = 500t. Maturity amount from Bank A = 10000+500t10000 + 500t.

Interest from Bank B: IB=(10000+500t)×0.06×5=3000+150tI_B = (10000 + 500t) \times 0.06 \times 5 = 3000 + 150t.

Given ratio IAIB=1013\frac{I_A}{I_B} = \frac{10}{13}: 500t3000+150t=1013\frac{500t}{3000 + 150t} = \frac{10}{13} 50t300+15t=1013  ⟹  13t=60+3t  ⟹  10t=60  ⟹  t=6\frac{50t}{300 + 15t} = \frac{10}{13} \implies 13t = 60 + 3t \implies 10t = 60 \implies t = 6

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