Question

A shopkeeper sold sarees at Rs. 226 each after giving 5% discount on labelled price. Had he not given the discount, he would have earned a profit of 12% on the cost price. What was the cost price of each saree?
a. Rs. 240
b. Rs. 260
c. Rs. 280
d. Data inadequate
e. None of these

Answer 1

Hint: First, we will assume the marked price of the saree as x. Then, we will find the marked price of saree by using the formula, x - 5% of x = 266. And we know that profit percentage on cost price is 12%, so we will find the cost price of saree using the formula, $CP=\dfrac{100}{100+\text{Profit}\%}\times MP$, where, CP is the cost price and MP is the marked price.

Complete step-by-step answer:
It is given in the question that, a shopkeeper sold sarees at Rs. 226 each after giving 5% discount on labelled price. Had he not given the discount, he would have earned a profit of 12% on the cost price. And we have been asked to find the cost price of each saree.
Let us assume the marked price of the saree as Rs. x. And it is said that, the shopkeeper had given a discount of 5% on the marked price and then he sold the saree at Rs. 266. So, the marked price can be calculated as,
x – 5%of x = 266
$\begin{align}
  & x-\dfrac{5x}{100}=266 \\
 & \dfrac{100x-5x}{100}=266 \\
 & \dfrac{95x}{100}=266 \\
\end{align}$
On cross multiplying, we get,
$\begin{align}
  & 95x=26600 \\
 & x=\dfrac{26600}{95} \\
 & x=280 \\
\end{align}$
Thus, we get the marked price of each saree as Rs. 280.
Now, we know that the shopkeeper earned a profit of 12% on the cost price. So, the cost price can be calculated by using the formula,
$CP=\dfrac{100}{100+\text{Profit}\%}\times MP$
On substituting the values of profit percentage as 12 and the marked price (MP)
 As Rs. 280, we will get the cost price (CP) as,
$\begin{align}
  & CP=\dfrac{100}{100+12}\times 280 \\
 & =\dfrac{100}{112}\times 280 \\
 & =\dfrac{25}{28}\times 280 \\
 & =25\times 10 \\
 & =250 \\
\end{align}$
Thus, the cost price of each saree will be Rs. 250.
Hence, option (e) is the correct answer.

Note: The possible mistake that the students can make in this question is that, they consider the formula for finding the cost price as $CP=\dfrac{100}{100+\text{Profit}\%}\times SP$ and hence, they will get the answer as Rs. 237.5, and this is wrong. So, the students are advised to use the correct formula, that is, $CP=\dfrac{100}{100+\text{Profit}\%}\times MP$ in order to get the correct answer. Also, some students may write as 5% of x = 266, But this is wrong, as the price after discount will be, the original price – the discounted price, hence, the condition should be written as x – 5% of x = 266.