Question
The simple interest and compound interest (compounded
yearly) on a sum Rs. ‘P’ at ‘r%’ p.a. for two years are Rs. 18,000 and Rs. 19,350, respectively. If the same principal is invested at simple interest of (r + 9)% p.a., find the interest earned in 27 months.Solution
ATQ, (2Pr/100) = 18,000 …… (I) P{(1 + r/100)² − 1} = 19,350 ⇒ P[(r/100)² + 2r/100] = 19,350 …… (II) Subtract (I) from (II): (Pr²/10000) = 19,350 − 18,000 = 1,350 …… (III) Divide (I) by (III): [(2Pr/100)] / [(Pr²/10000)] = 18,000 / 1,350 = 13⅓ ⇒ 200/r = 13⅓ ⇒ r = 15 From (I): (2P·15/100) = 18,000 ⇒ P = 60,000 Required SI at (r + 9)% for 27 months (i.e., 2.25 years): Rate = 24% p.a. Interest = P × (24/100) × 2.25 = 60,000 × 0.24 × 2.25 = Rs. 32,400
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