Question

A trader buys some T-shirts at 10 % rebate on the printed price of Rs. 450 per piece. For a long time he could not sell any T-shirt, so he sells it for Rs. 360 per piece. What amount of profit or loss per piece does he make? How much percentage of rebate does the customer earn?
A. Loss Rs. 70, 20 % rebate
B. Loss Rs. 45, 30 % rebate
C. Loss Rs. 45, 20 % rebate
D. Loss Rs. 55, 10 % rebate

Answer 1

Hint: We will first find the cost price of 1 T-shirt after a rebate of 10 % from the printed price as, $Rs\left( 450-\dfrac{10}{100}\times 450 \right)$. After that we will compare the cost price with the selling price. If the selling price or SP is greater than the cost price or CP, then there is a profit and if the CP is greater than SP, then there is a loss. The rebate percentage of the customer can be calculated as, $\dfrac{\text{Amount of total rebate}}{\text{Printed price}}\times 100$.

Complete step-by-step answer:
It is given in the question that a trader buys some T-shirts at 10 % rebate on the printed price of Rs. 450 per piece. As the trader does not sell any T-shirt for a long time, he sells the T-shirt for Rs. 360 per piece. We have been asked to find the amount of profit or loss he makes per piece and also the percentage of rebate earned by the customer.
So, we have the printed price of the T-shirt = Rs. 450.
And, we have the amount that the trader sells the T-shirt for as = Rs. 360.
We know that the trader got a rebate of 10 % on the printed price while purchasing the T-shirt. So, the amount of rebate received by the trader will be,
$\begin{align}
  & =10\%\text{ of Rs }450 \\
 & \Rightarrow \dfrac{10}{100}\times 450 \\
 & \Rightarrow 0.1\times 450 \\
 & \Rightarrow \text{Rs }45 \\
\end{align}$
So, we get the cost price of a T-shirt for the trader = (Printed price - rebate price), which is equal to Rs. (450 - 45) = Rs. 405.
So, the cost price of 1 T-shirt for the trader = Rs. 405. Now, it is clear that Rs. 405 is greater than Rs. 360. This means that the selling price of 1 T-shirt is less than the cost price of 1 T-shirt. Thus, we can say that it is a loss for the trader. We can calculate the loss amount by subtracting the cost price of 1 T-shirt from the selling price of 1 T-shirt.
So, we get the loss amount on 1 T-shirt = Rs. (405 - 360) = Rs. 45. Now, if we find the actual amount of rebate earned by the customer during this purchase, then it would be = (Printed price - selling price), which is equal to Rs. (450 - 360) = Rs. 90. So, we can find the rebate percentage earned by the customer as,
$\begin{align}
  & =\dfrac{\text{Amount of total rebate}}{\text{Printed price}}\times 100 \\
 & \Rightarrow \dfrac{90}{450}\times 100 \\
 & \Rightarrow \dfrac{100}{5} \\
 & \Rightarrow 20\% \\
\end{align}$
Thus, the customer earned a rebate of 20 %.
Therefore, the correct answer is option C, loss of Rs. 45, 20 % rebate.

Note: Most of the students make a mistake while finding the rebate amount earned by the customer. They may subtract the cost price of 1 T-shirt with the cost price of 1 T-shirt of the trader, that is Rs. (405 - 360) = Rs. 45. And as a result they may get the rebate percentage as 10 %, which is incorrect. The rebate amount is calculated as, (Printed price - selling price) and not as (Cost price - selling price).