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Question
A man sells an article at a profit of 25%. If he had bought it at 10% less and sold it for Rs 7 less, he would have gained 35%. Find the cost price of the article.
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Solution
Let ₹ ‘x’ be the C.P. of the article
∴ The article was sold at 25% profit
∴ S.P. of the article = `"x"(1 + 25/100)`
= `"x"(1 + 1/4)`
= `"x" xx 5/4`
= 1.25 x
If the article was bought at a 10% loss
i.e. the new C.P. = `"x"(1 - 10/100)`
= `"x"(9/10) = 0.9"x"`
and sold at ₹ 7 less
∴ New S.P. = 1.25 x – 7
Then, the profit would have been 35%
Using profit percentage = `("S.P. - C.P.")/"C.P." xx 100`
∴ `35 = ((1.25"x" - 7) - 0.9"x")/(0.9"x") xx 100`
∴ `35/100 = (0.35"x" - 7)/(0.9"x")`
∴ `7/20 = (0.35"x" - 7)/(0.9"x")`
∴ 6.3x = 20(0.35x - 7)
∴ 6.3x = 7x − 140
∴ 7x − 6.3x = 140
∴ 0.7x = 140
∴ x = `140/0.7`
∴ x = 200
∴ Cost price of the article is ₹ 200
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