An article is sold at $20 %$ profit. If is cost price is increased by Rs. $50$ and at the same time if its selling price is also increases by Rs. $30$ , the percentage of profit decrease by $\frac{10}{3} %$ . Find the cost price.

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Solution

Let the cost price be Rs. $100 x$
$20 %$ profit means selling price is Rs. $120 x$ .
New cost price $=$ Rs. $(100 x + 50)$
New selling price $=$ Rs. $(120 x + 30)$
New profit $= (120 x + 30) - (100 x + 50) =$ Rs. $20 x - 20$
$20 %$ less $\frac{10}{3} %$ $= \frac{50}{3} %$
$\Rightarrow \frac{20 x - 20}{100 x + 50} = \frac{50}{\frac{3}{100}} = \frac{1}{6}$
On cross multiplying, we have
$120 x - 120 = 100 x + 50$
$\Rightarrow 20 x = 170$
$\Rightarrow x = 8.5$
Therefore, cost price is Rs. $850$ .

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