The compound interest on a certain sum of money for 2 years at 10% per annum is Rs. 525.The simple interest on the same sum of money for double the time at half the rate percent per annum is ?

Answer: Option B

Let the sum of money be rs. P
Then,
$$\begin{array}{rl}& \Rightarrow \left[P{\left(1+\frac{R}{100}\right)}^t-P\right]=\text{C}\text{.I}\text{.}\\ & \Rightarrow \left[P{\left(1+\frac{10}{100}\right)}^2-P\right]=525\\ & \Rightarrow P{\left(\frac{11}{10}\right)}^2-1=525\\ & \Rightarrow P\left(\frac{121}{100}-1\right)=525\\ & \Rightarrow P\left(\frac{21}{100}\right)=525\\ & \Rightarrow P=\frac{525\times 100}{21}\\ & \Rightarrow P=\text{Rs}\text{.}2500\\ & \therefore \text{ Sum of money}\\ & \text{ = Rs}\text{. 2500}\end{array}$$
Simple interest on the same sum Rs. 2500 for 4 (double the time) years at 5% (half the rate of percent per annum) is
So,
$$\begin{array}{rl}& \text{S}\text{.I}\text{. = Rs}\text{.}\left(\frac{2500\times 5\times 4}{100}\right)\\ & \text{ = Rs}\text{. 500}\end{array}$$