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:

Solution (By Examveda Team)

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