Question

A milkman brought milk at $Rs{\text{ }}40.00$per liter and sold it at $Rs{\text{ }}50.00$per liter. Find his gain percentage.

Answer 1

Hint: If you are buying something for $Rs{\text{ X}}$and selling it for $Rs{\text{ Y}}$. If $Y > X$(SP$ > $CP), then you are in the profit. Profit made = gain = SP $ - $CP( $Rs{\text{ X - }}Rs{\text{ Y}}$) and profit percentage = gain percent = $\dfrac{{gain}}{{CP}} \times 100$. Similarly, if $X > Y$(CP$ > $SP), then you are in loss. Loss = CP $ - $SP ( $Rs{\text{ Y - }}Rs{\text{ X}}$) and loss percent = $\dfrac{{loss}}{{CP}} \times 100$.

Complete solution by step:
In this question, the cost price of milk = CP = $Rs{\text{ }}40.00$
Selling price of milk = SP = $Rs{\text{ }}50.00$
Clearly, SP$ > $CP
It means the milkman has made profit.
Profit = (selling price $ - $ cost price) = SP$ - $CP = $Rs{\text{ 50 - }}Rs{\text{ 40 = }}Rs{\text{ 10}}$
So, gain = $Rs{\text{ 10}}$
Percentage gain means to express the profit or gain in form of percentages.
$\therefore $percentage gain = $\dfrac{{gain}}{{CP}} \times 100$
Here, gain = $Rs{\text{ 10}}$
CP = $Rs{\text{ }}40$
Substituting the values in the above formula of calculating percentage gain,
$\because $percentage gain = $\dfrac{{gain}}{{CP}} \times 100$
$ \Rightarrow $percentage gain = $\dfrac{{10}}{{40}} \times 100$$\% $= $25\% $

Hence, the gain percentage of the shopkeeper is $25\% $.

Note:
If the selling price and cost price is the same (SP = CP), then there is no loss or gain. We can decide whether the person has loss or gain from percentage also.
We take the formula of percentage as percentage = $\dfrac{{SP - CP}}{{CP}} \times 100$
If the percentage we get is positive then we can say that he has made profit and if the percentage is negative then we can say that he has loss.
Let us suppose that the percentage of milkman is $'y'$
Now, by using the above formula,
$
   \Rightarrow y = \dfrac{{50 - 40}}{{40}} \times 100 \\
   \Rightarrow y = 25\% \\
 $
Here, the value of percentage is positive. It means the milkman has made a profit and profit percentage is $25\% $.