Question

A cloth merchant, on selling 44 metres of cloth, gets a profit equal to the selling price of 22 metres of the cloth. Find his profit percentage.

Answer 1

Hint: First, we should know the formula of the profit(P) which is the subtraction of the cost price(CP) of the item from the selling price(SP) of the item. Then, by using the condition given in the question, we get SP of 22 metres of cloth=CP of 44 metres of cloth. Then, we suppose that the CP of 1 metre of cloth be Rs. 1. After that, we should know the formula to calculate profit(P)% as $ P\%=\dfrac{SP-CP}{CP}\times 100 $ to get the value of the profit percentage.

Complete step-by-step answer:
In this question, we are supposed to find the profit percentage of the cloth merchant on selling 44 metres of cloth.
So, we should know the formula of the profit(P) which is a subtraction of the cost price(CP) of the item from the selling price(SP) of the item.
Now, in this question, we get this condition as:
SP of 44 metres of cloth-CP of 44 metres of cloth=profit(P)
Also, there is a condition given in the question which gives the value of profit as SP of 22 metres of cloth.
So, by substituting the value of profit in the above expression, we get:
SP of 44 metres of cloth-CP of 44 metres of cloth=SP of 22 metres of cloth
Now, by solving the above equation, we get the following relation as:
SP of 22 metres of cloth=CP of 44 metres of cloth
Now, let us suppose that the CP of 1 metre of cloth be Rs. 1.
Then, we get the CP of 22 metres of cloth is:
 $ 22\times 1=22 $
So, CP of 22 metres of cloth is Rs. 22.
Now, by using the condition, SP of 22 metres of cloth=CP of 44 metres of cloth we get the value of SP of 22 metres of cloth as:
SP of 22 metres of cloth is:
 $ 44\times 1=44 $
So, SP of 22 metres of cloth is Rs. 44.
Now, we should know the formula to calculate profit(P)% as:
 $ P\%=\dfrac{SP-CP}{CP}\times 100 $
So, by using the above formula, we get:
 $ \begin{align}
  & P\%=\dfrac{44-22}{22}\times 100 \\
 & \Rightarrow P\%=\dfrac{22}{22}\times 100 \\
 & \Rightarrow P\%=100 \\
\end{align} $
So, the profit percentage is 100%.
Hence, on selling 44 metres of cloth, gets a profit equal to the selling price of 22 metres of the cloth the merchant gets the profit percentage as 100%.

Note: In these types of the questions, we must be aware of the basic formulas of the profit and loss percent so that SP and CP given in the questions must be used appropriately to get the final result. So, the formulas for the two where P is profit and L is loss are:
 $ \begin{align}
  & P\%=\dfrac{SP-CP}{CP}\times 100 \\
 & L\%=\dfrac{CP-SP}{CP}\times 100 \\
\end{align} $