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 ?

Explanation:-

Let the sum of money be rs. P
Then, $$\eqalign{ & \left[ {P{{\left( {1 + \frac{R}{{100}}} \right)}^t} - P} \right] = {\text{C}}{\text{.I}}{\text{.}} \cr & \left[ {P{{\left( {1 + \frac{{10}}{{100}}} \right)}^2} - P} \right] = 525 \cr & \Rightarrow P{\left( {\frac{{11}}{{10}}} \right)^2} - 1 = 525 \cr & \Rightarrow P\left( {\frac{{121}}{{100}} - 1} \right) = 525 \cr & \Rightarrow P\left( {\frac{{21}}{{100}}} \right) = 525 \cr & \Rightarrow P = \frac{{525 \times 100}}{{21}} \cr & \Rightarrow P = {\text{Rs}}{\text{.}}\,2500 \cr & \therefore {\text{ Sum of money}} \cr & {\text{ = Rs}}{\text{. 2500}} \cr}$$ 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, $$\eqalign{ & {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left( {\frac{{2500 \times 5 \times 4}}{{100}}} \right) \cr & \,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 500}} \cr}$$