Question

A furniture seller sold two dressing tables at the rate of $ Rs.7200 $ . Out of them $ 20\% $ profit obtained on one table and $ 20\% $ loss on another. How much profit or gain percentage is obtained in the whole transaction?

Answer 1

Hint: To find the profit or loss gain we should know the cost price and selling price. So we will find the cost price of both furniture and then if the total cost of furniture is more than selling price then it is profit otherwise loss.

Complete step by step answer:
Moving ahead with the question in step-to-step manner
Selling price of furniture is $ Rs.7200 $
 $ 20\% $ profit and loss is made on each furniture respectively.
Let the cost price of 1^st furniture be x, then according to the question seller had made $ 20\% $ profit on it and sold it at $ Rs.7200 $ i.e.
 $ 7200=x+20\%ofx $
So solving it further we will get;
 $ \begin{align}
  & 7200=x+\dfrac{20x}{100} \\
 & 7200=x+\dfrac{x}{5} \\
\end{align} $
By taking LCM we will get;
 $ \begin{align}
  & 7200=\dfrac{5x+x}{5} \\
 & 7200=\dfrac{6x}{5} \\
 & x=\dfrac{7200\times 5}{6} \\
 & x=6000 \\
\end{align} $
So cost price of 1^st furniture is $ 6000Rs. $
Similarly cost price for 2^nd furniture, for which we know that seller had sold it at the loss of $ 20\% $ which is $ Rs.7200 $ . Let the cost price of 2^nd furniture be ‘y’.
So according to the question seller had made $ 20\% $ loss on it and sold it at $ Rs.7200 $ i.e.
 $ 7200=y-20\%ofy $
So solving it further we will get;
 $ \begin{align}
  & 7200=y-\dfrac{20y}{100} \\
 & 7200=y-\dfrac{y}{5} \\
\end{align} $
By taking LCM we will get;
 $ \begin{align}
  & 7200=\dfrac{5y-y}{5} \\
 & 7200=\dfrac{4y}{5} \\
 & y=\dfrac{7200\times 5}{4} \\
 & y=9000 \\
\end{align} $
So the cost of 2^nd furniture is $ 9000Rs. $
Now to find profit or loss gain, Total Selling price $ - $ Total cost price, if it is positive then there is profit otherwise it is loss.
So total selling price is equal to sum of sold price of both furniture i.e. $ 7200+7200=14400Rs. $
And total cost price is the sum of cost price of both furniture i.e. $ 6000+9000=15000Rs. $
So profit or loss gain is equal to Total Selling price $ - $ Total cost price i.e. $ 14400-15000=-600 $
As it is negative means seller had gain loss of $ Rs.600 $
For loss percentage we know that loss percentage $ =\dfrac{\text{Loss }\!\!~\!\!\text{ Amount}}{\text{Total }\!\!~\!\!\text{ Cost }\!\!~\!\!\text{ prize}}\times 100 $
So loss percentage is equal to;
 $ \dfrac{600}{15000}\times 100=4\% $
So there is $ 4\% $ loss.
Hence the answer is $ 4\% $ loss.

Note: For calculating the profit and loss we are required to know the cost price from which we will compare the cost price and selling price, if the selling price is more than it is profit, and if it is less than it is loss.