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 :

Let the sum = Rs. $$100x$$

For compound interest, rate of interest (r) = 10% and time (t) = 2 years

=> $$C.I. = P[(1+\frac{r}{100})^t-1]$$

=> $$100x[(1+\frac{10}{100})^2-1]=525$$

=> $$100x[(\frac{11}{10})^2-1]=525$$

=> $$100x \times (\frac{121-100}{100})=525$$

=> $$21x=525$$

=> $$x=\frac{525}{21}=25$$

$$\therefore$$ Sum invested = Rs. 2500

For simple interest, rate of interest (r) = 5% and time (t) = 4 years

=> $$S.I.= \frac{P \times r \times t}{100}$$

= $$\frac{2500 \times 5 \times 4}{100}$$

= $$25 \times 20=Rs.$$ $$500$$

=> Ans - (C)