The simple interest on a certain sum of money for three years at 8% per annum is half the compound interest on Rs 4000 for 2 years at 10% per annum. The sum placed on simple interest is:

To solve this problem, we first need to calculate the compound interest on Rs 4000 for 2 years at 10% per annum.

The formula for compound interest is:

A = P (1 + r/n)^(nt)

Where: A = the amount of money accumulated after n years, including interest. P = the 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

In this case, P = 4000, r = 10/100 = 0.1, n = 1 (since it's compounded annually), and t = 2.

So, A = 4000 (1 + 0.1/1)^(1*2) = 4000 * (1.1)^2 = 4000 * 1.21 = Rs 4840.

The compound interest is then A - P = 4840 - 4000 = Rs 840.

The problem states that the simple interest for three years is half of this, so the simple interest is 840/2 = Rs 420.

The formula for simple interest is I = PRT/100, where I is the interest, P is the principal, R is the rate, and T is the time.

We know I = 420, R = 8, and T = 3. We want to find P.

So, 420 = P83/100.

Solving for P gives P = 420 / (8*3/100) = Rs 1750.

So, the sum placed on simple interest is Rs 1750.