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      Question

      Selling price of a cap is at 10% profit, and that of a

      scarf is 25%. If total profit on selling 6 caps and 3 scarves is Rs. 48, and on selling 4 caps and 5 scarves is Rs. 65, what is the cost price of a cap?
      A Rs.20 Correct Answer Incorrect Answer
      B Rs.56 Correct Answer Incorrect Answer
      C Rs.40 Correct Answer Incorrect Answer
      D Rs.25 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let CP of cap = 100x, scarf = 100y

      SP of cap = 110x, scarf = 125y

      Profit:

      6(110x) + 3(125y) – 6(100x) – 3(100y) = 48

      ⇒ 60x + 75y = 48 ……… (1)

      4(110x) + 5(125y) – 4(100x) – 5(100y) = 65

      ⇒ 40x + 125y = 65 ……… (2)

      (1) × 2 → 120x + 150y = 96

      (2) × 3 → 120x + 375y = 195

      Subtract:

      -225y = -99 ⇒ y = 0.44

      Put in (1):

      60x + 75 × 0.44 = 48

      ⇒ 60x + 33 = 48 ⇒ x = 0.25

      CP of cap = 100x = Rs. 25

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