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A shopkeeper marks his goods 30% above the cost price and gives a discount of 15% on the market price. What gain or loss did he make?

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10.5%

11%

11.5%

10%

answer is A.

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Detailed Solution

Concept- First, we will assume the cost price as Rs. x. The cost is increased by 30% and then decreased by 15% to get the final selling price. Then, we will find profit or loss by the relation

(Profit or Loss % = \frac{(SP - CP)}{CP} \times 100)

.
Assume the cost price of the good = Rs. x.
First, we will find the marked price of the good,

MP = x + (\frac{30}{100} \times x)

\Rightarrow x + 0.3 x = 1.3 x

MP = 1.3 x

SP = MP - (\frac{15}{100} \times MP)

Substitute the values in the above formula,

\Rightarrow SP = 1.3 x - (\frac{15}{100} \times 1.3 x)

\Rightarrow SP = 1.3 x - (0.15 \times 1.3 x)

\Rightarrow SP = 1.3 x - (0.195 x)

\Rightarrow SP = 1.105 x

Now, using the Profit / Loss% formula

(Profit or Loss % = \frac{(SP - CP)}{CP} \times 100)

\Rightarrow \frac{1.105 x - x}{x} \times 100 %

\Rightarrow \frac{0.105 x}{x} \times 100 %

\Rightarrow 0.105 \times 100 %

\Rightarrow 10.5 %

SP > CP , therefore gain
∴ The shopkeeper will get a gain of 10.5%.
Hence, the correct option is 1.

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