A certain sum of money is divided into two parts.

Solution

ATQ, Let the amount invested at 20% CI = P₁ Amount invested at 10% SI = P₂ Interest from P₁ at 20% CI: 2 years: P₁[(1.2)² − 1] = P₁(1.44 − 1) = 0.44P₁ 3 years: P₁[(1.2)³ − 1] = P₁(1.728 − 1) = 0.728P₁ Interest from P₂ at 10% SI: 2 years: 0.20P₂ 3 years: 0.30P₂ Given: (1) 0.44P₁ + 0.20P₂ = 27,600 (2) 0.728P₁ + 0.30P₂ = 44,120 Subtract (1) from (2) by first forming the “extra 1 year” equation: Extra interest in 3rd year = 44,120 − 27,600 = 16,520 This extra interest = (0.728 − 0.44)P₁ + (0.30 − 0.20)P₂ ⇒ 0.288P₁ + 0.10P₂ = 16,520 …(A) We also have: 0.44P₁ + 0.20P₂ = 27,600 …(B) Multiply (A) by 2: 0.576P₁ + 0.20P₂ = 33,040 …(C) Subtract (B) from (C): (0.576 − 0.44)P₁ = 33,040 − 27,600 0.136P₁ = 5,440 P₁ = 5,440 / 0.136 = 40,000 From (B): 0.44×40,000 + 0.20P₂ = 27,600 17,600 + 0.20P₂ = 27,600 0.20P₂ = 10,000 ⇒ P₂ = 50,000 Total amount = P₁ + P₂ = 40,000 + 50,000 = Rs 90,000