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. 400Rs. 500Rs. 600Rs. 800

The compound interest (CI) formula is:

CI = P(1 + r/n)^(nt) - P

Where: P = principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years

Given: CI = Rs. 525 for 2 years at 10% per annum. So, r = 10/100 = 0.1, t = 2, n = 1 (since it's annually), and we need to find P.

525 = P(1 + 0.1/1)^(12) - P 525 = P(1.1)^2 - P 525 = P1.21 - P 525 = 0.21P P = 525 / 0.21 P = Rs. 2500

Now, we need to find the simple interest (SI) on the same sum (P = Rs. 2500) for double the time (t = 2*2 = 4 years) at half the rate (r = 0.1/2 = 0.05).

The simple interest formula is:

SI = Prt

So, SI = 25000.054 = Rs. 500

Therefore, the simple interest on the same sum for double the time at half the rate percent per annum is Rs. 500.