# Had a trader bought an item at 10% less and sold it at 10% more, he would have doubled his profit percentage.

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Had a trader bought an item at 10% less and sold it at 10% more, he would have doubled his profit percentage. What was the original profit percentage?

$\frac{200}{7}\%$ should be the right answer.

Let the original buying price be X Rupees, and let the original selling price be $(X \times Y)$ Rupees.

Then the original profit will be $(Y - 1).100\%$.

Now if we drop buying price by $10\%$ it will become $(0.9 X)$ Rupees and if we increase selling price by $10\%$ it will become $(1.1 .(X.Y))$, & the modified profit will be $\frac{(1.1 Y - 0.9)}{0.9}\times 100\%$.

It is given that

$$2.(Y - 1) = \frac{1.1 Y - 0.9}{0.9}$$

On solving this we get $Y = \frac{9}{7}$,

so the original profit percentage $= \left(\frac{9}{7} - 1\right).100 = \frac{200}{7}\%$

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