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An article is sold at a certain price. By selling it at $\frac{2}{3}$ that price one loses $10 % .$ Find the gain percent at original price.

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31 %

23 %

35 %

45 %

answer is C.

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Detailed Solution

Let,
Cost price, CP=100 Rs.
Given,

loss, l = 10 %

It is known that,
Selling price= cost price- loss
Selling price

= 100 - \frac{10}{100} \times 10

Selling price = 100 - 10 = 90 Rs

Now, selling price is

\frac{2}{3}

of original price. Thus, original price,

= 90 \times \frac{3}{2} = 135 Rs.

Now, the profit percentage,

P % = \frac{135 - 100}{100} \times 100

P % = 35

%
This is the required gain percentage.
Hence, option 3 is correct.

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