Multiple choice

The rates of simple interest in two banks x and y are in the ratio of 10 : 8. Rajini wants to deposit her total savings in two banks in such a way that she receives equal half-yearly interest from both. She should deposit the savings in banks x and y in the ratio of

  1. 4 : 5

  2. 3 : 5

  3. 5 : 4

  4. 2 : 1

  5. None of these
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A Correct answer
Explanation

Let the interest rates be 10k and 8k, and the amounts deposited be P1 and P2. For equal interest, P1 * 10k = P2 * 8k, which simplifies to P1/P2 = 8/10 = 4/5.

AI explanation

The ratio of the interest rates for bank x and bank y is 10 to 8, or 5 to 4. Because Rajini receives equal half-yearly interest from both banks, the product of the principal and the interest rate must be equal for both, meaning Principal x multiplied by Rate x equals Principal y multiplied by Rate y. This implies that the ratio of the principals is the inverse of the ratio of the rates, which is 4 to 5.

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