Question

By selling a T-shirt for Rs. 648 a shopkeeper faces a loss of 4%. For how much should he sell the T-shirt to make a gain of 4%?

Answer 1

Hint: Start by letting the cost price of the T-shirt to be x. It is given that the shopkeeper faced a loss of 4% when he sold the T-shirt for Rs. 648, using this form a mathematical equation and finding the value of x. Once you get x, add 4% of x to the value of x to get the answer.

Complete step by step solution:
Let us start the solution to the above question by letting the cost price of the T-shirt to be Rs. x. Now as it is given that the T-shirt was sold by the shopkeeper at the cost of Rs. 648 due to which he faced a loss of 4%.
$\text{selling price}=\text{cost price}-\text{loss}$
$\Rightarrow 648=x-4\%\text{ of }x$
$\Rightarrow 648=x-\dfrac{4}{100}x$
$\Rightarrow 648=\dfrac{96}{100}x$
Now we will take 96 and 100 to the other side of the equation. On doing so, we get
 $\Rightarrow 648\times \dfrac{100}{96}=x..........(i)$
Now we know the cost price of the T-shirt. We are asked to find the price at which the T-shirt needs to be sold so that the seller makes a profit of 4%. So, we will add the value of profit, i.e., 4% of x to x to get the answer.
$SP=CP+profit$
$\Rightarrow SP=x+\dfrac{4}{100}x$
Now we will put the value of x from equation (i). On doing so, we get
$SP=\dfrac{648\times 100}{96}+\dfrac{4}{100}\times \dfrac{648\times 100}{96}$
Now we will take $\dfrac{648\times 100}{96}$ common. On doing so, we get
\[SP=\dfrac{648\times 100}{96}\left( 1+\dfrac{4}{100} \right)\]
\[\Rightarrow SP=\dfrac{648\times 100}{96}\left( \dfrac{100+4}{100} \right)\]
\[\Rightarrow SP=\dfrac{648\times 100}{96}\left( \dfrac{104}{100} \right)=\text{Rs}\text{. 702}\]

Hence, we can conclude that the shopkeeper must sell the T-shirt at Rs. 702 to make a profit of 4%.

Note: Don’t get confused and calculate the profit with respect to SP instead of CP. Also, remember the price given in the question is the selling price for which the seller faced the loss of 4% and is not the cost price of the seller. Be careful in the calculation part as well and try not to convert the fractions into the decimal form until it is the last option to do, because in fractional form it is easier to cancel out the factors.