A lent ₹ 5000 to B for 2 years and ₹ 3000 to C for 4 years on simple interest at the same rate of interest and received ₹ 2200 in all from both of them as interest. The rate of interest per annum is
(a)5\%
(b)7\%
(c)$7 \frac{1}{8} \%$
(d)10\%
Answer
Answer (as printed): D
Explanation
Let the rate be R\% p.a. Then, $$\begin{aligned} & \left(\frac{5000 \times R \times 2}{100}\right)+\left(\frac{3000 \times R \times 4}{100}\right)=2200 \\ & \Leftrightarrow \quad 100 R+120 R=2200 \Rightarrow R=\left(\frac{2200}{220}\right)=10 . \\ & \therefore \quad \text { Rate }=10 \% . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.