A sum of money amounts to Rs.12,000 after 6 years and Rs.15,000 after 9 years at the same rate of simple interest. What is the rate of interest per annum?

Correct option is C

Given:

Amount after 6 years = Rs.12000,

Amount after 9 years = 15000.

Formula Used:

$$\text{SI} = \text{Amount} - \text{Principal}, \\ \ \\ \text{Rate} = \frac{100 \times \text{SI}}{P \times T}$$ 

where, P = Principle, T = time, 

Solution:
Difference in amounts after 9 and 6 years = 15000 - 12000 = 3000.
This is the interest for 3 years.

​$$\text{Annual Interest} = \frac{3000}{3} = 1000$$​​

Principal P = 12000 - 6000 = 6000  

Putting the values in the formula;

​$$1000 = \frac{6000 \times R \times 1}{100} \\ \ \\ \quad \Rightarrow \quad R = \frac{1000 \times 100}{6000} = \frac{100000}{6000} = 16 \frac{2}{3} \%$$