Question

On simple interest a certain sum amounts to ₹14061 in 6 years and to ₹16023 in 8 years on the same rate of interest. The rate of interest per annum is:

• A. 9%
• B. 10%
• C. 12%
• D. 14%

Hint:

Difference in amounts = interest for difference in years

Answer 1

The Correct Option is C

Step 1: Find interest for 2 years.
Amount after 8 years = ₹16023.
Amount after 6 years = ₹14061.
Interest for 2 years = \(16023 - 14061 = 1962\). Step 2: Find interest per year.
Interest per year = \(\frac{1962}{2} = 981\). Step 3: Find principal.
Principal = Amount after 6 years − interest for 6 years.
Interest for 6 years = \(6 \times 981 = 5886\).
Principal = \(14061 - 5886 = 8175\). Step 4: Find rate of interest.
Rate = \(\frac{\text{Annual Interest}}{\text{Principal}} \times 100 = \frac{981}{8175} \times 100\).
\(981 \div 8175 = 0.12\).
Rate = \(0.12 \times 100 = 12%\).