 QUESTION

# A shopkeeper marks his goods 50% above the cost price. If he gives a discount of 10%, then find his gain percent.

Hint: Here we go through by first assuming the cost price of goods as some variable then add the given percentage to the cost price and at the end subtract the discount % after that apply the formula gain% to find the answer.

Here in the question it is given that a shopkeeper marks his goods 50% above the cost price.
Let us assume the cost price of goods is Rs. X.
And now we calculate the market price i.e. 50% above the cost price that means,
$= \left( {50\% {\text{ }}of{\text{ }}x} \right) + x \\ = \dfrac{{50}}{{100}} \times x + x \\ = \dfrac{{3x}}{2} \\$

Now it is given that the shopkeeper gives a 10% discount on market price I.e.
$= \dfrac{{3x}}{2} - \left( {10\% {\text{ }}of{\text{ }}\dfrac{{3x}}{2}} \right) \\ = \dfrac{{3x}}{2} - \dfrac{{10}}{{100}} \times \dfrac{{3x}}{2} \\ = \dfrac{{30x - 3x}}{{20}} \\ = \dfrac{{27x}}{{20}} \\$
Hence the selling price is $\dfrac{{27x}}{{20}}$

Now we have to find gain%. And we know that the formula of gain% is $\dfrac{{S.P - C.P}}{{C.P}} \times 100$ here S.P means selling price and C.P means cost price.
After putting the value in formula we get,
$= \dfrac{{\dfrac{{27x}}{{20}} - x}}{x} \times 100 \\ = \dfrac{7}{{20}} \times 100 \\ = 35\% \\$

Hence the gain is 35% to the shopkeeper.

Note:- Whenever we face such a type of question the key concept for solving the question is to first have to calculate the market price then apply the discount percentage on them. Some mistakes that students make here is to subtract the discount percent directly from the raised percent and from the result percentage they make the selling price . This is the wrong process u will get the wrong answer. So the better way of solving the question is defined above.