Out of Rs. 15,000, 'X' invested a part of it on compound interest at 20% p.a. (compounded annually) for 2 years and the remaining amount on simple interest at 15% p.a. for 2 years. If the total interest earned by him was Rs. 5,760, then determine the simple interest earned by him.

ATQ,

Let the amount invested by 'X' on compound interest be Rs. ‘p’. Then, amount invested by 'X' on simple interest = Rs. (15,000 – p) Simple interest = Principal × Rate × Time ÷ 100 Simple interest earned = (15,000 – p) × 15 × 2 ÷ 100 = Rs. (4,500 – 0.3p) Compound interest = Principal × (1 + Rate ÷ 100)² – Principal Compound interest = p × (1.2)² – p ⇒ Compound interest = 1.44p – p = 0.44p ATQ: 0.44p + 4,500 – 0.3p = 5,760 ⇒ 0.14p = 1,260 ⇒ p = 9,000 Amount invested on simple interest = 15,000 – 9,000 = 6,000 Simple interest earned = 6,000 × 0.15 × 2 = Rs.1,800