CAT 2024 Slot 1 QA Q12 Interest

Question 12 of the Quantitative Ability (QA) section, CAT 2024 Slot 1, with CAT's official answer and a worked solution.

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) 6 Interest MCQ

Solution

  1. Interest from A over \(t\) years: \(10000 \times 5\% \times t = 500t\). Maturity amount \(= 10000 + 500t\).
  2. Interest from B: \((10000 + 500t) \times 6\% \times 5 = 3000 + 150t\).
  3. \(\frac{500t}{3000 + 150t} = \frac{10}{13} \Rightarrow 6500t = 30000 + 1500t \Rightarrow t = 6\).

Shortcut. Test the options: \(t = 6\) gives 3000 and 3900, ratio 10 : 13.

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