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      Question

      A shopkeeper bought a certain number of identical books

      at ₹120 each. He sold: 30% of them at a profit of 25% each, 40% of them at a profit of 10% each, and the remaining books at a loss of 20% each. His overall profit was ₹990. How many books did he buy?
      A 120 Correct Answer Incorrect Answer
      B 100 Correct Answer Incorrect Answer
      C 150 Correct Answer Incorrect Answer
      D 200 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let total number of books = n Cost price per book = ₹120 Total CP = 120n First 30% of n: 0.30n books at 25% profit Profit/book = 25% of 120 = 0.25 × 120 = ₹30 Profit₁ = 0.30n × 30 = 9n Next 40% of n: 0.40n books at 10% profit Profit/book = 10% of 120 = 12 Profit₂ = 0.40n × 12 = 4.8n Remaining 30% of n: 0.30n books at 20% loss Loss/book = 20% of 120 = 24 Loss₃ = 0.30n × 24 = 7.2n Net profit = Profit₁ + Profit₂ − Loss₃ = 9n + 4.8n − 7.2n = 6.6n Given net profit = ₹990 ⇒ 6.6n = 990 ⇒ n = 990 / 6.6 = 150

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