A shopkeeper sells two items, A and B. Item B’s cost price is twice as that of item A. The shopkeeper sells item A at 10% profit and item B at 20% profit. Which one of the following is the value of net profit ?
[amp_mcq option1=”15%” option2=”13.33%” option3=”18%” option4=”16.66%” correct=”option4″]
This question was previously asked in
UPSC CAPF – 2024
Let the cost price of item B be CP_B.
Given: CP_B = 2 * CP_A.
For calculation, let CP_A = ₹100.
Then CP_B = 2 * ₹100 = ₹200.
Total Cost Price = CP_A + CP_B = ₹100 + ₹200 = ₹300.
Item A is sold at 10% profit.
Profit on A = 10% of CP_A = 10% of ₹100 = ₹10.
Selling Price of A (SP_A) = CP_A + Profit on A = ₹100 + ₹10 = ₹110.
Item B is sold at 20% profit.
Profit on B = 20% of CP_B = 20% of ₹200 = ₹40.
Selling Price of B (SP_B) = CP_B + Profit on B = ₹200 + ₹40 = ₹240.
Total Selling Price = SP_A + SP_B = ₹110 + ₹240 = ₹350.
Net Profit = Total Selling Price – Total Cost Price = ₹350 – ₹300 = ₹50.
Net Profit Percentage = (Net Profit / Total Cost Price) * 100
Net Profit Percentage = (₹50 / ₹300) * 100
Net Profit Percentage = (1/6) * 100 = 100/6 = 50/3 = 16.66…%.
Let CP_A = x. Then CP_B = 2x. Total CP = 3x.
SP_A = x + 0.10x = 1.1x.
SP_B = 2x + 0.20(2x) = 2x + 0.4x = 2.4x.
Total SP = 1.1x + 2.4x = 3.5x.
Net Profit = Total SP – Total CP = 3.5x – 3x = 0.5x.
Net Profit Percentage = (0.5x / 3x) * 100 = (0.5 / 3) * 100 = (1/6) * 100 = 16.66…%.
This is a weighted average profit. Item B has twice the cost price of A, so its profit contributes twice as much to the total profit in absolute terms. The overall profit percentage is closer to the profit percentage of the more expensive item.