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:

Rs. 400

Rs. 500

Rs. 600

Rs. 800

Explanation:

Let the sum be Rs. P.

Then,$ \left[P\left(1 +\dfrac{10}{100} \right)^2- P\right] $= 525

$\Rightarrow$P$ \left[\left(\dfrac{11}{10} \right)^2- 1\right] $= 525

$\Rightarrow$ P =$ \left(\dfrac{525 \times 100}{21} \right) $= 2500.

$\therefore$ Sum = Rs . 2500.

So, S.I. = Rs.$ \left(\dfrac{2500 \times 5 \times 4}{100} \right) $= Rs. 500