A shopkeeper marks his goods 20% higher above the cost price and also gives a discount of 10%. Find his gain percent.

*x*.

Then, 20% of

*x*is $\frac{20x}{100}\mathrm{i}.\mathrm{e}.\frac{x}{5}$

According to the parenthesis, the marked price is 20% higher above the cost price.

This means, marked price of goods = $x+\frac{x}{5}=\frac{6x}{5}$

Now, 10% of $\frac{6x}{5}$ is $\frac{6x}{5}\times \frac{10}{100}=\frac{6x}{50}$

Again according to the parenthesis, the shopkeeper gives 10% discount.

Then, Selling price of goods = $\frac{6x}{5}-\frac{6x}{50}=\frac{60x-6x}{50}=\frac{54x}{50}$

Then, net gain = selling price - cost price = $\frac{54x}{50}-x=\frac{4x}{50}$

So, gain percentage = $\frac{\mathrm{net}\mathrm{gain}\times 100}{\mathrm{cost}\mathrm{price}}=\frac{{\displaystyle \frac{4x}{50}}\times 100}{x}=\frac{4x\times 100}{50x}=8\%$

Therefore gain percent is 8%.

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