CAT 2024 Slot 1 · Quant · Question 12

CAT 2024 Slot 1 previous year question on Simple Interest and Compound Interest, with the answer and a step-by-step solution.

Simple Interest and Compound InterestArithmeticMultiple choiceMedium
An amount of ₹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
Pick an option, then check.
Answer & solution

Answer: Option C

Let the money stay in bank A for t years.

Simple interest in bank A is 10000\times \frac{5}{100}\times t=500t.

The maturity amount moved to bank B is 10000+500t.

Simple interest in bank B over 5 years is \left( 10000+500t \right)\times \frac{6}{100}\times 5=0.3\left( 10000+500t \right).

That is 3000+150t.

The ratio of the two interests is 10:13, so \frac{500t}{3000+150t}=\frac{10}{13}.

Cross-multiplying, 6500t=30000+1500t.

So 5000t=30000 and t=6 years.

Shortcut. Bank B's interest is always 30\% of whatever is deposited, since 6\% for 5 years is simple interest. Writing it as 0.3\times \left( \text{maturity}\right) removes a step and keeps the equation linear.

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