Question

If an article is sold for Rs.178 at a loss of 11%. What should be its selling price in order to earn a profit of 11%?
A. Rs.222.50
B. Rs.267
C. Rs.222
D. Rs.220

Answer 1

First of all, find out the cost price of the article by using the given data and the formula {\text{C}}{\text{.P}} = \dfrac{{{\text{S}}{\text{.P}}}}{{100 - {\text{Loss% }}}} \times 100. Then find out the selling with a profit of 11% by using the formula {\text{S}}{\text{.P}} = \dfrac{{100 + {\text{Profit% }}}}{{100}} \times {\text{C}}{\text{.P}}. So, use this concept to reach the solution of the given problem.

Complete step-by-step answer :
Given that the article is sold for Rs.178 at a loss of 11%.
So, selling price of article = Rs.178
Loss percent = 11%
We know that {\text{C}}{\text{.P}} = \dfrac{{{\text{S}}{\text{.P}}}}{{100 - {\text{Loss% }}}} \times 100
So, cost price of the article $= \dfrac{{178}}{{100 - 11}} \times 100 = \dfrac{{178}}{{89}} \times 100 = 2 \times 100 = {\text{Rs}}.200$
Now, we have to find the selling price of the article in order to get a profit of 11%
We know that, {\text{S}}{\text{.P}} = \dfrac{{100 + {\text{Profit% }}}}{{100}} \times {\text{C}}{\text{.P}}
So, selling price of the article to have profit of 11% $= \dfrac{{100 + 11}}{{100}} \times 200$
$$
= \dfrac{{111 \times 200}}{{100}} \\
= 111 \times 2 \\
= {\text{Rs}}{\text{.222}} \\

$$Hence, to gain a profit of 11**Thus, the correct option is C. Rs.222** **Note** : There is a loss whenever the cost price of the article is greater than the selling price of the article. And there is a profit whenever the selling price of the article is greater than the cost price of the article.$$