When a shopkeeper sells item A for ₹ 384, then there is a loss of 20% and when…
2023
When a shopkeeper sells item A for ₹ 384, then there is a loss of 20% and when he sells item B for ₹ 400, then there is a profit of 25%. What is the profit/loss percent, if he sells both items for a total of ₹ 852?
- A.
Profit, 6.5%
- B.
Loss, 5%
- C.
Loss, 7%
- D.
Profit, 7.5%
Show answer & explanation
Correct answer: A
Concept: If an article is sold at a loss of r%, its cost price is CP = SP / (1 - r/100); if sold at a profit of r%, CP = SP / (1 + r/100). When two items are sold together, the overall profit or loss percent is worked out from the combined cost price and the combined selling price: Overall % = ((Total SP - Total CP) / Total CP) x 100.
Cost price of item A: SP = ₹384 with a loss of 20%, so CP(A) = 384 / (1 - 20/100) = 384 / 0.80 = ₹480.
Cost price of item B: SP = ₹400 with a profit of 25%, so CP(B) = 400 / (1 + 25/100) = 400 / 1.25 = ₹320.
Combined cost price: CP(A) + CP(B) = 480 + 320 = ₹800.
Combined selling price when both items are sold together, as given in the question, is ₹852.
Overall profit = Combined SP - Combined CP = 852 - 800 = ₹52.
Overall profit percent = (52 / 800) x 100 = 6.5%.
Cross-check: a profit of 6.5% on the combined cost price of ₹800 gives 800 x 1.065 = ₹852, which matches the combined selling price stated in the question, confirming an overall profit of 6.5%.