Question

A certain sum of money is invested at an interest rate of 5% P.A. and a second sum of money, which is twice as large as the first, is invested at 5.5% P.A. The total interest on investments together is ₹1000 per year. The first sum of money invested is:

• A. ₹6250
• B. ₹12500
• C. ₹10500
• D. ₹11500

Hint:

In problems involving simple interest, the total interest is the sum of individual interests from each sum, which can be calculated using the respective rates.

Answer 1

The Correct Option is A

Let the first sum of money be x. - The interest on the first sum invested at 5% per annum will be: \[ \text{Interest} = \frac{5}{100} \times x = 0.05x \] - The second sum is twice the first sum, so it is 2x. - The interest on the second sum invested at 5.5% per annum will be: \[ \text{Interest} = \frac{5.5}{100} \times 2x = 0.11x \] The total interest is ₹1000, so: \[ 0.05x + 0.11x = 1000 \] \[ 0.16x = 1000 \] \[ x = \frac{1000}{0.16} = 6250 \] Thus, the first sum of money invested is ₹6250.