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A man sells two articles for тВ╣42000 each. He gets a profit of 45% on one article and loses 45% on the other article. What is his overall profit or loss (to the nearest integer) in this transaction? 1693
тВ╣21329 profit
тВ╣21429 profit
тВ╣21329 loss
тВ╣21429 loss
тВ╣21329 loss
When selling price of two articles is same and profit% equals loss%, the overall result is always a loss equal to (x2/100)%. Here, (452/100)=20.25% total loss on the total investment.
Selling Price of each article (SP) = тВ╣42000, Profit percent (p) = 45%, Loss percent (l) = 45%.
Loss%=100x2тАЛ
When selling price of two articles is same and profit% equals loss%, the overall result is always a loss equal to (x2/100)%. Here, (452/100)=20.25% total loss on the total investment.
Students often assume no profit or loss because +45% and -45% cancel out, but this ignores that the base price for profit and loss is different.
Calculate Cost Prices
Cost Price 1 (CP1тАЛ) = 42000/1.45=28965.52 and Cost Price 2 (CP2тАЛ) = 42000/0.55=76363.64.
CPTotalтАЛ=28965.52+76363.64=105329.16
Calculate Total Selling Price
Total Selling Price (SPTotalтАЛ) = 42000+42000.
SPTotalтАЛ=84000
Calculate Total Loss
Loss = CPTotalтАЛтИТSPTotalтАЛ=105329.16тИТ84000.
Loss=21329.16тЙИ21329
C is correct because the total cost price is approximately тВ╣105329 and total selling price is тВ╣84000, resulting in a loss of тВ╣21329.
This concept of 'Constant Selling Price with equal percentage Gain/Loss' is a standard variation of the Successive Percentage Change topic in Competitive Quantitative Aptitude.
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