A certain sum is invested on compound interest (compounded annually) amounts to Rs.5040 in three years. If the rate of interest is 20% for the first year, 40% for the second year and 50% for the third year, then what is the value of the sum?

Let P be the principal. After 1st year at 20%: P × 1.20. After 2nd year at 40%: P × 1.20 × 1.40 = P × 1.68. After 3rd year at 50%: P × 1.68 × 1.50 = P × 2.52. Final amount is Rs.5040, so P × 2.52 = 5040, giving P = 5040 / 2.52 = Rs.2000. Verification: 2000 × 1.20 = 2400, then 2400 × 1.40 = 3360, then 3360 × 1.50 = 5040. The calculation checks out.