Question
Answers

If all the articles are 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
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Hint: Assume the actual value of the article to be \[x\] so\[\dfrac{11}{100}x\] will be 11% of \[x\].
Now if we say that we sell it on 11% profit it means that our selling price will be $ x+\dfrac{11}{100}x $
And if we say that we sell it on 11% loss it means that our selling price will be $ x-\dfrac{11}{100}x $

Complete step-by-step answer:
First scenario, we sold for 178Rs at a loss of 11%, we can write this in mathematical form as
\[x-\dfrac{11}{100}x=178\]
 \[\to \dfrac{100-11}{100}x=178\]
On further solving we get
 \[\to \dfrac{89}{100}x=178\]
\[\to x=200\]
So the Actual price of the article is 200Rs.
Second scenario, to find the selling price if we sell it at 11% profit, we can write this in mathematical form as
Assuming our selling price as \[a\].
\[x+\dfrac{11}{100}x=a.......(2)\].
\[\to \dfrac{(100+11) x}{100} =a\]
\[\to \dfrac{(111) x}{100}=a..........(3)\]
Now to calculate the value of \[a\] we have to put the value of \[x\] in equation (3).
On putting \[x=200\] in equation (3) we get our equation as
\[\dfrac{111(200)}{100}=a\]
Which on solving gives \[a=222\]
Conclusion, actual value of article is Rs 200 after selling it on 11% loss it becomes Rs 178 and on selling it on 11% profit it becomes Rs 222.
So, the correct answer is “Option C”.

Note: Always use this basic approach to solve profit loss questions, If there is an option 200 in the MCQ and you are in shortage of time, then you might have marked 200 as the final answer because you calculate the value of x as 200 but always read your question carefully that is what the question is asking.