A man sells an article at $5 %$ above its cost price. If he had bought it at $5 %$ less than what he paid for it and sold it for $R s . 2$ less, he would have gained $10 % .$ Find the cost price of the article.

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Solution

Let original Cost price of $1$ article $C P 1 = R s x$
Then Selling price of the article $= S P 1 = \frac{100 + 5}{100} x = \frac{105}{100} x$

=> If he had bought it for $5$ % less, then $C P 2 = \frac{100 - 5}{100} x = \frac{95}{100} x$
And sold it for $R s 2$ less, then $S P 2 = R s \frac{105}{100} x - 2$
Given Profit % $= \frac{S . P .2 - C . P .2}{C . P .2} \times 100 = 10$
$=> \frac{\frac{105}{100} x - 2 - \frac{95}{100} x}{\frac{95}{100} x} \times 100 = 10$
$=> \frac{10 x - 200}{95 x} \times 100 = 10$
$=> 10 x - 200 = 9.5 x$
$=> 0.5 x = 200$
$x = 400$
Thus, C.P. 1 $= R s 400$

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A man sells an article at 5% above its cost price. If he had bought it at 5% less than what he paid for it and sold it for Rs.2 less, he would have gained 10%. Find the cost price of the article.

A man sells an article at $5 %$ above its cost price. If he had bought it at $5 %$ less than what he paid for it and sold it for $R s . 2$ less, he would have gained $10 % .$ Find the cost price of the article.