Question

The cost price of an article is 30% less than its selling price. Find, profit or the loss as a percentage.
A) \[{\text{41}}\dfrac{{\text{6}}}{{\text{7}}}{\text{% }}\] loss
B) \[{\text{40}}\dfrac{{\text{6}}}{{\text{7}}}{\text{% }}\] loss
C) \[{\text{43}}\dfrac{{\text{6}}}{{\text{7}}}{\text{% }}\] gain
D) \[{\text{42}}\dfrac{{\text{6}}}{{\text{7}}}{\text{% }}\] gain

Answer 1

Hint: let the selling price be x. Now, for cost price use the condition as per mentioned in the question that it is 30% less than it’s selling price. And use both the calculated cost price and selling price in the formula of calculation of profit or loss.

Complete step by step solution:
Let the product’s ${\text{S}}{\text{.P = X}}$ ----(1)
And so as it is given in the question that cost price is 30% less than the selling price so cost price will be
\[{\text{C}}{\text{.P = }}\]\[X - \dfrac{{30}}{{100}}X\]-----(2)
\[{\text{ = 0}}{\text{.7X}}\]
Now ,formula of profit/ loss in percentage can be stated as
=\[\dfrac{{{\text{S}}{\text{.P - C}}{\text{.P}}}}{{{\text{C}}{\text{.P}}}}{\text{(100)}}\] ----(3)
use (1) and (2) in the equation (3)
= \[{\text{}}\dfrac{{{\text{X - 0}}{\text{.7X}}}}{{{\text{0}}{\text{.7X}}}}{\text{(100)}}\]
\[{\text{ = }}\dfrac{{{\text{300}}}}{{\text{7}}}{\text{% }}\]
Thus , \[\dfrac{{300}}{7}\% \] is the increased percentage we can obtained all through the above calculation. And it states that it is a profit .
On factorizing the above,
\[ = 42\dfrac{6}{7}\% \]
As the percentage is positive, it is profit.
Option (D) is the correct answer.

Note: In the case of profit, always the Selling price of an article is greater than its cost price, Whereas in case of loss the Cost price of an article is greater than its Selling price. In some questions terms, Marked price is also given, Marked price is the MRP of an article, it can be same as selling price or not. It is always given on marked price and the discounted amount is the selling price of an article.