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