Question

# The price of a pair of trousers was decreased by 22% to ${$30}$. What was the original price of the trousers?A.28.5B.24.6C.38.5D.None of these Answer Verified Hint: We take the original price of the trouser to be x. Then it is given that the reduced price of trouser is${$30}$, that will be given by x – 22% of x , we can obtain the required solution by solving the equation.

In the question we are told that the price of the trousers has decreased by 22% to ${$30}$. And we are asked to find the original price of the trousers. Now, let us assume that the original price of the trousers before the price reduction equals to ‘x’. Then the decreased price, that is the price after reduction is given by subtracting the reduced amount from the original amount) It is given that the decreased price is${$30}$
Therefore, we have the equation
$x - 22\% \times x = 30$ (1)
Here we know that, $22\% = \dfrac{{22}}{{100}} = 0.22$
Now we can rewrite the equation (1) as
$x - 0.22x = 30$
$0.78x = 30$
Dividing the whole equation with 0.78, we get
$x = \dfrac{{0.78}}{{30}}$
$x \approx 38.46 \approx 38.5$
Thus, the original price of the trousers was ${$38.5}\$.
Hence the correct answer is option C.

Note: An error that may occur in this problem is that we may take the 22% of the reduced money and add it to the reduced money to get the original price, that is a wrong approach for this question. This problem has real-life applications such as buying things at an offer and then calculating the original price to find out how much was the profit.