Question

By selling $ 33 $ meters of cloth, one gains the selling price of $ 11 $ meters. Find the gain percent.

Answer 1

Hint: We shall analyze the given information so that we are able to solve the problem. We are given a condition that by selling $ 33 $ meters of cloth, one is able to gain the selling price of $ 11 $ meters. Using this condition, we need to obtain a relation between cost price and the selling price. Then, we need to substitute the obtained relation in the formula of gain percent.
Formula to be used:
a) The formula to calculate the gain/profit is as follows.
 $ \text{Profit} = SP - CP $
b) The formula to calculate the gain percent is as follows.
 \[Gain{\text{ }}percent = \dfrac{{SP - CP}}{{CP}} \times 100\]
Where SP is the selling price and CP is the cost price.

Complete step by step answer:
Let us consider the cost price of the cloth as CP and the selling price of the cloth as SP.
Then, we can see that the cost price of $ 33 $ meters of cloth is $ 33CP $ and the selling price of $ 33 $ meters of cloth is $ 33SP $ .
Now, we shall calculate the profit of selling $ 33 $ meters of cloth.
Using the formula $ \text{Profit} = SP - CP $ , we have
 $ \text{Profit} = 33SP - 33CP $
  We are given a condition that by selling $ 33 $ meters of cloth, one is able to gain the selling price of $ 11 $ meters.
That is $ \text{Profit} = 33SP - 33CP = 11SP $
 $ \Rightarrow 33SP - 33CP = 11SP $
 $ \Rightarrow 33SP - 33CP - 11SP = 0 $
 $ \Rightarrow 22SP - 33CP = 0 $
 $ \Rightarrow 22SP = 33CP $
 $ \Rightarrow SP = \dfrac{{33}}{{22}}CP $
 $ \Rightarrow SP = \dfrac{3}{2}CP $
Now, we shall calculate the gain percent.
Using the formula \[Gain{\text{ }}percent = \dfrac{{SP - CP}}{{CP}} \times 100\] , we have the following.
We need to substitute $ SP = \dfrac{3}{2}CP $ in the formula.
Thus \[Gain{\text{ }}percent = \dfrac{{\dfrac{3}{2}CP - CP}}{{CP}} \times 100\]
We shall pick the common terms.
 $ \Rightarrow Gain{\text{ }}percent = \dfrac{{\left( {\dfrac{3}{2} - 1} \right)CP}}{{CP}} \times 100 $
 $ \Rightarrow Gain{\text{ }}percent = \dfrac{{\left( {\dfrac{1}{2}} \right)CP}}{{CP}} \times 100 $
 $ \Rightarrow Gain{\text{ }}percent = \left( {\dfrac{1}{2}} \right) \times 100 $
 $ \Rightarrow Gain{\text{ }}percent = 50\% $
Hence, the required gain percent is $ 50\% $ .

Note: Here, we are not given the selling price and cost price directly. So we calculate a relation between them. If the selling price and cost price are given directly, we need to substitute them in the formula of gain percent.
Similarly, if loss percent is asked to calculate, use the formula \[Loss{\text{ }}percent = \dfrac{{CP - SP}}{{CP}} \times 100\]