Question

A sum becomes rs 720 after 2 years and rs 1020 after 7 years at simple interest. The rate of interest per annum is:

• A. 10%
• B. 9%
• C. 8%
• D. 11%

Hint:

To find the rate of interest, subtract the two amounts and divide the difference by the number of years, then solve for the rate.

Answer 1

The Correct Option is A

Let the principal be \( P \) and the rate of interest be \( R \). Using the formula for Simple Interest: \[ \text{Amount} = P + \frac{P \times R \times T}{100} \] For 2 years, we have: \[ 720 = P + \frac{P \times R \times 2}{100} \quad \text{(Equation 1)} \] For 7 years, we have: \[ 1020 = P + \frac{P \times R \times 7}{100} \quad \text{(Equation 2)} \] Subtract Equation 1 from Equation 2: \[ 1020 - 720 = \left( \frac{P \times R \times 7}{100} \right) - \left( \frac{P \times R \times 2}{100} \right) \] \[ 300 = \frac{P \times R \times 5}{100} \] \[ 300 \times 100 = P \times R \times 5 \] \[ 30000 = P \times R \times 5 \] \[ P \times R = 6000 \quad \text{(Equation 3)} \] Substitute this value into Equation 1: \[ 720 = P + \frac{6000 \times 2}{100} \] \[ 720 = P + 120 \] \[ P = 600 \] Substitute \( P = 600 \) into Equation 3: \[ 600 \times R = 6000 \] \[ R = 10% \text{ per annum} \]