Question

The profit earned by selling an article for Rs.900 is double the loss incurred when the same article is sold for the Rs.450. At what price should the article be sold?
A.Rs.750
B.Rs.800
C.Rs.600
D.Rs.900

Answer 1

Hint: Cost price is the price at which we buy an article whereas selling price is the price at which we sell an article.
Profit=Selling price-Cost price.

Complete step-by-step answer:
\[Profit{\text{ }}percentage = \left[ {\dfrac{{\left( {selling{\text{ }}price - cost{\text{ }}price} \right)}}{{\left( {cost{\text{ }}price} \right)}}} \right] \times 100\]
\[ = \left[ {\dfrac{{profit}}{{cost{\text{ }}price}}} \right] \times 100\]
Loss=Cost price-Selling price.
 Let’s say P is the profit if we sell the article at 900rupees.
\[ \Rightarrow P = 900 - Cost{\text{ }}price........\left( 1 \right)\]
Let’s say L is the loss if we sell the article at 450rupees.
\[ \Rightarrow L = Cost{\text{ }}price - 450.........\left( 2 \right)\]
Given that the profit earned by selling an article for 900rupees is double the loss incurred when the same article is sold for 450rupees.
\[ \Rightarrow P = 2L......\left( 3 \right)\]
Substitute 1 and 2 in 3
\[ \Rightarrow \left( {900 - cost{\text{ }}price} \right) = 2\left( {cost{\text{ }}price - 450} \right)\]
\[ \Rightarrow {\text{ }}900 - cost{\text{ }}price = 2\left( {cost{\text{ }}price} \right) - 900\]
\[ \Rightarrow 1800 = 3\left( {cost{\text{ }}price} \right).\]
Therefore, the cost price of the article is 600 rupees.

To make a profit of 25%, we should sell the article at S rupees.
Since, \[profit{\text{ }}\left( \% \right) = \left[ {\dfrac{{\left( {selling{\text{ }}price - costprice} \right)}}{{\left( {cost{\text{ }}price} \right)}}} \right] \times 100\] and cost price=600 rupees.

\[ \Rightarrow \;25 = \left[ {\dfrac{{\left( {S - 600} \right)}}{{\left( {600} \right)}}} \right] \times 100\]
\[ \Rightarrow 150 = S - 600\]
\[ \Rightarrow S = 750.\]
Therefore, to make a profit of 25%, we should sell the article at 750 rupees, i.e, option A.

Note: Profit is the return we get for investing in the article. Profit percentage is the percentage of investment we gain by selling the article. Loss is the return we lose for investing in the article. Loss percentage is the percentage of investment we lose by selling the article.