Question

A man borrowed Rs 500 at the rate of 3% p.a. and Rs 600 at 4.5% p.a. on simple interest, with an agreement that the whole sum will be returned only if the total sum becomes Rs 1520. The number of years after which the borrowed sum is to be returned is:

• A. 5
• B. 7
• C. 10
• D. 12

Hint:

When calculating interest and total sum, use the formula for simple interest and solve for the unknown variable.

Answer 1

The Correct Option is C

Let the number of years be \( t \). The simple interest for the first loan is: \[ \text{SI}_1 = \frac{500 \times 3 \times t}{100} = 15t \] The simple interest for the second loan is: \[ \text{SI}_2 = \frac{600 \times 4.5 \times t}{100} = 27t \] The total sum at the end of \( t \) years is: \[ \text{Total sum} = 500 + 600 + 15t + 27t = 1100 + 42t \] We are given that the total sum becomes 1520: \[ 1100 + 42t = 1520 \] \[ 42t = 1520 - 1100 = 420 \] \[ t = \frac{420}{42} = 10 \] Thus, the number of years is 10.