Question
A man invests ₹50,000 in a business. After 2 years, he
sells 30% of his stake for a 40% profit and reinvests the amount. After another year, he sells 25% of his remaining stake at a 50% profit and reinvests half of the profit. At the end of 4 years, he sells the rest of his stake, which has appreciated by 35%. What is the total value of his investment at the end of 4 years?Solution
Initial investment = ₹50,000. First sale after 2 years: 30% of ₹50,000 = ₹15,000. Profit = ₹15,000 × 40% = ₹6,000. Reinvested amount = ₹15,000 + ₹6,000 = ₹21,000. Remaining stake after 1st sale = ₹50,000 - ₹15,000 = ₹35,000. Second sale after 3 years: 25% of ₹35,000 = ₹8,750. Profit = ₹8,750 × 50% = ₹4,375. Reinvested amount = ₹8,750 + ₹2,187.5 (half the profit) = ₹10,937.5. Remaining stake after 2nd sale = ₹35,000 - ₹8,750 = ₹26,250. Appreciation after 4 years = ₹26,250 × 35% = ₹9,187.5. Final value of remaining stake = ₹26,250 + ₹9,187.5 = ₹35,437.5. Total value = ₹21,000 + ₹10,937.5 + ₹35,437.5 = ₹67,375. Plus profit reinvested earlier = ₹6,000 + ₹4,375 = ₹10,375. Final value = ₹67,375 + ₹10,375 = ₹77,750. Closest option: a) ₹77,750.
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