A man sells an article as a gain of 5%. If he had sold it at Rs 63 less, he would have lost 2% . Find the cost of the article

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Solution

Let CP be the cost price of the article
SP be the selling price of the article.
Gain of the article ( in percentage)=5
$\Rightarrow \frac{S P - C P}{C P} \times 100 = 5$
$\Rightarrow S P - C P = \frac{5}{100} C P$
$\Rightarrow S P = \frac{5}{100} C P - C P = \frac{105}{100} C P$
$\Rightarrow S P = \frac{105}{100} C P .$
Loss in the article if he sold 63 rupees less
(in percentage)=2.
$\Rightarrow \frac{C P - (S P - 63)}{C P} \times 100 = 2$
$\Rightarrow C P - S P + 63 = \frac{2}{100} C P$ .
$\Rightarrow C P - \frac{105}{100} C P - \frac{2}{100} C P = - 63$
$\Rightarrow (1 - \frac{105}{100} - \frac{2}{100}) C P = - 63$
$\Rightarrow (\frac{100 - 107}{100}) C P = - 63$
$\Rightarrow C P = - 63 \times \frac{100}{- 7}$
$\Rightarrow C P = 900$
Thus cost price of the article = Rs 900.

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