A man sells two T.V.s at the same rate. In case of first T.V. he makes 10%…
2015
A man sells two T.V.s at the same rate. In case of first T.V. he makes 10% profit and in case of second one he loses 10%. Then his loss or gain percent is
- A.
1% profit
- B.
5% profit
- C.
1% loss
- D.
no loss no profit
Show answer & explanation
Correct answer: C
Concept: When an article is sold at the same selling price once at x% profit and once at x% loss, the two transactions never cancel out — the overall result is always a loss equal to (x/10)2 percent of the combined cost price, regardless of the actual selling price used.
Application: Let the common selling price of each T.V. be SP.
For the first T.V., a 10% profit means SP = CP1 × 1.10, so CP1 = SP / 1.10 = 10·SP/11.
For the second T.V., a 10% loss means SP = CP2 × 0.90, so CP2 = SP / 0.90 = 10·SP/9.
Total cost price = CP1 + CP2 = 10·SP/11 + 10·SP/9 = SP × (90 + 110)/99 = 200·SP/99.
Total selling price = SP + SP = 2·SP = 198·SP/99.
Since total CP (200·SP/99) is greater than total SP (198·SP/99), the deal produces a net loss = 200·SP/99 − 198·SP/99 = 2·SP/99.
Loss% = (Loss / Total CP) × 100 = (2·SP/99) ÷ (200·SP/99) × 100 = 1%.
Cross-check: Using the shortcut identity for equal-selling-price profit/loss pairs, loss% = (x/10)2 with x = 10 gives (10/10)2 = 12 = 1%, confirming the step-by-step result independently.
Result: The overall transaction is a net loss of 1%.