A lent Rs. 4000 to B for 2 years and Rs. 2000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is :

14%

15%

12%

13.75%

Explanation:

Let the rate of interest per annum be R%

Simple Interest for Rs.4000 for 2 years at R% + Simple Interest for Rs.2000 for 4 years at R%

= 2200

$\dfrac{4000 \times \text{R} \times 2}{100} + \dfrac{2000 \times \text{R} \times 4}{100} = 2200$

80$\text{R} + 80 \text{R} $= 2200

160$\text{R} = 2200$

16$\text{R} = 220$

4$\text{R} = 55$

$\text{R} = \dfrac{55}{4} = 13.75\%$