To solve this problem, we can use the formula for calculating simple interest:

simple interest = (principal x rate x time) / 100

We are given that the simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on 400 for 2 years at 10% per annum. We can express this as follows:

(principal x 8% x 3 years) / 100 = (400 x 10% x 2 years) / 100 / 2

Simplifying the right-hand side of the equation gives us:

(principal x 8% x 3 years) / 100 = (400 x 10% x 2 years) / 200

We can then solve for the principal by multiplying both sides of the equation by 200:

(principal x 8% x 3 years) / 100 x 200 = (400 x 10% x 2 years)

Simplifying the left-hand side of the equation gives us:

principal x 16% x 3 years = 400 x 10% x 2 years

Dividing both sides of the equation by (16% x 3 years) gives us:

principal = (400 x 10% x 2 years) / (16% x 3 years)

Solving for the principal gives us:

principal = 600

Therefore, the sum of money placed on simple interest is 600.