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A shopkeeper sells two articles for тВ╣1000 each. On one he gains 20% and on the other he loses 20%. Find the net gain/loss percentage.
4% loss
4% gain
No profit, no loss
2% loss
4% loss
When selling two items at the same price with equal percentage profit and loss (x%), a net loss always occurs, calculated directly as (x/10)2 percent.
Selling price of each article = тВ╣1000, Profit on first article = 20%, Loss on second article = 20%
Net┬аLoss%=(10xтАЛ)2
When selling two items at the same price with equal percentage profit and loss (x%), a net loss always occurs, calculated directly as (x/10)2 percent.
Students mistakenly assume there is no profit and no loss because the percentage gains and losses are equal in magnitude.
Identify Given Conditions
We are given that two articles are sold at the same price (SP=тВ╣1000 each) with equal profit and loss percentages (x=20%).
SP1тАЛ=SP2тАЛ=тВ╣1000,x=20%
Apply Shortcut Formula
For articles sold at equal selling prices with equal gain and loss percentages, use the standard net loss percentage formula.
Loss%=(1020тАЛ)2=22=4%
Verify via Cost Price Calculation
Calculate individual cost prices: CP1тАЛ=1.21000тАЛ and CP2тАЛ=0.81000тАЛ, giving total CP=2083.33 and total SP=2000, confirming a 4% loss.
Total┬аCP=2083.33,Total┬аSP=2000
A is correct because selling two articles at the same price with an equal percentage of gain and loss always results in a net loss of 4%.
This shortcut is a classic application of algebraic percentages, frequently tested in time-bound exams like RRB JE and SSC CGL to save calculation time.
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