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A man sells two chairs for тВ╣900 each. On one he gains 20% and on the other he loses 20%. What is his overall gain or loss percentage?
4% loss
4% gain
No profit no loss
2% loss
4% loss
When two items are sold at the same selling price, one at a profit of x% and the other at a loss of x%, there is always a net loss given by (x/10)^2\%.
Selling price of each chair = тВ╣900, Gain on first chair = 20%, Loss on second chair = 20%
Loss%=(10xтАЛ)2
When two items are sold at the same selling price, one at a profit of x% and the other at a loss of x%, there is always a net loss given by (x/10)^2\%.
Many students mistakenly assume that a 20% gain and a 20% loss cancel each other out, resulting in no profit and no loss.
Calculate Cost Price of the First Chair
Since the first chair is sold at a 20% gain for тВ╣900, we find its cost price CP1тАЛ using the formula SP=CP├Ч(1+100Gain%тАЛ)
CP1тАЛ=1.20900тАЛ=750
Calculate Cost Price of the Second Chair
Since the second chair is sold at a 20% loss for тВ╣900, we find its cost price CP2тАЛ using the formula SP=CP├Ч(1тИТ100Loss%тАЛ)
CP2тАЛ=0.80900тАЛ=1125
Calculate Total Cost Price and Total Selling Price
Add the individual cost prices and selling prices together to find the totals.
Total┬аCP=750+1125=1875,Total┬аSP=900+900=1800
Calculate Overall Loss Percentage
Determine the net loss and calculate the overall percentage loss relative to the total cost price.
Loss%=18751875тИТ1800тАЛ├Ч100=187575тАЛ├Ч100=4%
A is correct because the overall transaction results in a 4% loss.
This shortcut applies universally to any problem where two articles are sold at equal prices with identical percentage profit and loss margins.
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