Question

The price of a garment has reduced by \[15\% \] in a sale to Rs $306$ . Find the original price of the garment.
A) $320$
B) $360$
C) $380$
D) $340$

Answer 1

Hint:We will assume an arbitrary price for the garment initially. The price was reduced from that price so we will calculate the loss assuming the arbitrary price. Now we will subtract the loss from the original price and equate the result with the given price.

Complete step-by-step answer:
The given percentage loss is $15\% $ .
The price after the given loss is Rs $306$ that means that selling price is Rs $306$ .
Let us assume that the original price be Rs $x$ .
First, we will calculate the $15\% $ of $x$ as that will be the amount reduced totally.
$\dfrac{{15}}{{100}}x = \dfrac{3}{{20}}x$
Therefore, the reduction in Rs is $\dfrac{3}{{20}}x$ .
Now we have assumed that the original price was $x$ and it is reduced by the amount equal to $\dfrac{3}{{20}}x$ .
Therefore, after the reduction the final selling price will be the difference of these two amounts.
Thus, the selling price in terms of $x$ is:
$x - \dfrac{3}{{20}}x = \dfrac{{17}}{{20}}x$
It is given that the selling price of the same garment is in fact Rs $306$ .
But we just found that the selling price is $\dfrac{{17}}{{20}}x$.
Thus, from above two statements we conclude that these two quantities should be equal.
Thus, we will equate both the prices as follows:
$\dfrac{{17}}{{20}}x = 306$
On cross multiplying we get,
$17x = 6120$
Solve the above equation for $x$ as follows:
$x = 360$
Now $x$ is the original price of the given garment.
Therefore, the original price of the garment is Rs $360$ .

So, the correct answer is “Option B”.

Note:The solution is pretty clear but the important point is to note that the problem is about the loss and not profit. One can verify the answer by doing the given calculations.