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      Question

      The cost price of item β€˜P’ is Rs. 30 more than that

      of item β€˜Q’. Items β€˜Q’ and β€˜P’ are sold at a profit of 25% and a loss of 20%, respectively. If the total profit after selling both items is Rs. 10, then find the average cost price of items β€˜Q’ and β€˜P’ together.
      A Rs.375 Correct Answer Incorrect Answer
      B Rs.320 Correct Answer Incorrect Answer
      C Rs.335 Correct Answer Incorrect Answer
      D Rs.315 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the cost price of item β€˜Q’ = Rs. β€˜100y’ Then, cost price of item β€˜P’ = Rs. β€˜100y + 30’ Selling price of item β€˜Q’ = 100y Γ— 1.25 = Rs. β€˜125y’ Selling price of item β€˜P’ = (100y + 30) Γ— 0.8 = Rs. β€˜80y + 24’ So, overall profit = sum of selling prices – sum of cost prices = 125y + (80y + 24) – (100y + 100y + 30) = 205y + 24 – 200y – 30 = Rs. (5y – 6) So, 5y – 6 = 10 β‡’ 5y = 10 + 6 = 16 β‡’ y = 16 / 5 = 3.2 Average cost price of items β€˜Q’ and β€˜P’ together = (200y + 30) Γ· 2 = 100y + 15 = Rs. 100Γ—3.2 + 15 = Rs.335

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