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.

Answer 1

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) = 0.9x`

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 = ((1.25x - 7) - 0.9x)/(0.9x) xx 100`

∴ `35/100 = (0.35x - 7)/(0.9x)`

∴ `7/20 = (0.35x - 7)/(0.9x)`

∴ 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