Question
The cost price of item ‘P’ is Rs. 30 more than that
of item ‘Q’. Items ‘Q’ and ‘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 ‘Q’ and ‘P’ together.Solution
ATQ,
Let the cost price of item ‘Q’ = Rs. ‘100y’ Then, cost price of item ‘P’ = Rs. ‘100y + 30’ Selling price of item ‘Q’ = 100y × 1.25 = Rs. ‘125y’ Selling price of item ‘P’ = (100y + 30) × 0.8 = Rs. ‘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 ⇒ 5y = 10 + 6 = 16 ⇒ y = 16 / 5 = 3.2 Average cost price of items ‘Q’ and ‘P’ together = (200y + 30) ÷ 2 = 100y + 15 = Rs. 100×3.2 + 15 = Rs.335
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