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

Explanation:-

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