Question

Poorna bought 25 sarees at a discount of 20% and 1 saree was freely offered to her. Now she sells all the saree at the marked price to a customer. What is the profit percentage of retailer?
(a) 25%
(b) 30%
(c) 40%
(d) 20%

Answer 1

Hint: To solve this question, we will first assume some variable for the marked price of a single saree. Then, with the help of a unitary method, we will find the marked price of 25 sarees. We know that Poorna got the sarees at 25% of discount. Thus, we will find the cost price she has to pay to the seller. It is given that she got a saree for free. Thus, now she has 26 sarees and she sold all 26 sarees at the marked price. This will be the selling point. Once we got the selling price and cost price, we can find the percentage gain given by the relation $pg=\dfrac{sp-cp}{cp}\times 100\%$, where pg is percentage gain, sp is selling price and cp is the cost price.

Complete step-by-step answer:
Let the marked price of each saree be x.
According to the unitary method, if we know the cost of one unit and the number of units bought, then we can find the total cost as the product of cost of one unit and number of units bought.
Thus, the cost of 25 sarees will be 25x.
Now, it is given that Poorna got 25 sarees at 20% discount.
Therefore, the discount will be 20% of 25x. It is given as $25x\times \dfrac{20}{100}=5x$.
Therefore, the money Poorna had to pay the seller is the difference of the marked price and the discount.
$\Rightarrow $ cp = 25x – 5x
$\Rightarrow $ cp = 20x
Now, it is given that she got one saree for free. Therefore, Poorna got 26 sarees for 20x.
She sold these 26 sarees at their marked price.
Therefore, the selling price of 26 sarees will be the product of 26 and cost of one saree (x).
$\Rightarrow $ sp = 26x
We know that the percentage gain given by the relation $pg=\dfrac{sp-cp}{cp}\times 100\%$, where pg is percentage gain, sp is selling price and cp is the cost price.
$\begin{align}
  & \Rightarrow pg=\dfrac{26x-20x}{20x}\times 100\% \\
 & \Rightarrow pg=\dfrac{6}{20}\times 100\% \\
 & \Rightarrow pg=30\% \\
\end{align}$
Hence, option (b) is the correct option.

Note: This is an example of profit and loss. Prerequisites for this problem are concept of percentage and unitary method. Students are advised to be well versed with these concepts beforehand.