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      Question

      A shopkeeper marks an article 40% above its cost price.

      He allows a discount of x% on the marked price and still makes a profit of 12%. If, instead, he had allowed a discount of (x + 10)% on the marked price, his profit would have been Rs 56 less than before. What is the cost price of the article?
      A Rs 280 Correct Answer Incorrect Answer
      B Rs.300 Correct Answer Incorrect Answer
      C Rs 260 Correct Answer Incorrect Answer
      D Rs 400 Correct Answer Incorrect Answer
      E Rs 330 Correct Answer Incorrect Answer

      Solution

      Let cost price = C. Marked price = 40% above C = 1.4C. First scenario (discount x%, profit 12%): Selling price₁ = C * 1.12 Also, SP₁ = 1.4C * (1 − x/100) So: 1.4C * (1 − x/100) = 1.12C Divide by C (C > 0): 1.4(1 − x/100) = 1.12 1 − x/100 = 1.12 / 1.4 = 0.8 x/100 = 0.2 → x = 20% Second scenario (discount x + 10 = 30%): Selling price₂ = 1.4C * (1 − 30/100) = 1.4C * 0.7 = 0.98C Profit in first case > profit in second case by Rs 56: SP₁ − SP₂ = 56 1.12C − 0.98C = 56 0.14C = 56 C = 56 / 0.14 = 400 Cost price = Rs 400.

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