Question
The cost price of item βPβ is Rs. 30 more than that
of item βQβ. Items βQβ and βPβ 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 βQβ and βPβ together.Solution
ATQ,
Let the cost price of item βQβ = Rs. β100yβ Then, cost price of item βPβ = Rs. β100y + 30β Selling price of item βQβ = 100y Γ 1.25 = Rs. β125yβ Selling price of item βPβ = (100y + 30) Γ 0.8 = Rs. β80y + 24β So, overall profit = sum of selling prices β sum of cost prices = 125y + (80y + 24) β (100y + 100y + 30) = 205y + 24 β 200y β 30 = Rs. (5y β 6) So, 5y β 6 = 10 β 5y = 10 + 6 = 16 β y = 16 / 5 = 3.2 Average cost price of items βQβ and βPβ together = (200y + 30) Γ· 2 = 100y + 15 = Rs. 100Γ3.2 + 15 = Rs.335
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