Question

By selling an article for Rs 600 more, Karthik would have made a 5% profit on his sale instead of an 11% loss. What was his cost price?
A 3750
B 3650
C 3350
D 3950

Answer 1

Hint: Find the selling prices of the article, when Karthik made a 5% profit and 11% loss. Next, subtract the obtained selling prices and put it equal to 600.
Assume, the cost price of the given article as $x$.

Complete step-by-step solution -
If Karthik made 5%.profit on his sale; we can obtain the selling price of the article as shown below.
${\text{Selling price of the article}} = \left( {100 + 5} \right)\% \,of \,x \\$
$\Rightarrow {\text{Selling price of the article}} = 105\% \,of\,x \\$
$\Rightarrow {\text{Selling price of the article}} = 1.05\,x \\ $
Again, if Karthik made 11%.loss on his sale; we can obtain the selling price of the article as shown below.
 ${\text{Selling price of the article}} = \left( {100 - 11} \right)\% \,of\,x \\$
 $ \Rightarrow {\text{Selling price of the article}} = 89\% \,of\,x \\$
 $\Rightarrow {\text{Selling price of the article}} = 0.89\,x \\ $
According to the question,
  $1.05x - 0.89x = 600 \\$
  $\Rightarrow \,0.16x = 600 \\$
  $ \Rightarrow \,x = \dfrac{{600}}{{0.16}} \\$
  $\Rightarrow \,x = 3750 \\ $
Thus, the cost price of the article is Rs.3750; hence, option (A) is the correct answer.

Note: The difference in the selling prices of the article is equal to the increase in the price of the article. Students sometimes become confused with profit and gain, here profit and gain both are to be the same quantity. When the selling price is more than the cost price the seller earns gain/profit while if the cost price is more than the selling price the seller earns loss.