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Question
The percentage profit earned by selling an article for Rs. 2880 is equal to the percentage loss incurred by selling the same article for Rs. 1920. At what price the article should be sold to earn a 25% profit?
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Solution
Let x be C.P. of the article
Let y % be both, the gain and loss made when the article is sold at ₹ 2,880 and ₹ 1,920 respectively. Then
`"x" + "y"/100 "x" = 2880` ..........(i)
`"x" - "y"/100 "x" = 1920` .............(ii)
Adding (i) and (ii), we get
2x = 4800
∴ x = 2400
i.e. C.P. of the article = ₹ 2400
Required profit percentage = 25%
∴ S.P. = C.P.`[1 + "Profit%"/100]`
= `2400[1 + 25/100]`
= `2400[1 + 1/4]`
= `2400 xx 5/4`
= 3000
∴ The article should be sold at ₹ 3000 to earn 25% profit.
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