Question

A milkman bought milk at RS. 40.00/- per litre and sold it at RS. 50.00/- per litre then, find his gain or loss percentage.

Answer 1

Hint: We solve this problem first by finding whether the milkman has gain or loss.
We have the standard result that if the cost price is greater than the selling price then it is called as loss and if the cost price is less than the selling price then it is called as profit or gain
After finding the profit or loss we use the formula for the percentage.
The formula for gain percentage is given as
\[\text{gain percentage}=\dfrac{S.P-C.P}{C.P}\times 100\]
The formula for loss percentage is given as
\[\text{loss percentage}=\dfrac{C.P-S.P}{C.P}\times 100\]

Complete step by step answer:
We are given that the milkman bought milk at RS. 40/- per litre
Let us assume that the cost price of milk per litre as
\[\Rightarrow C.P=40\]
We are given that the milkman sold the milk at RS. 50/- per litre
Let us assume that the selling price of milk as
\[\Rightarrow S.P=50\]
We know that if the cost price is greater than the selling price then it is called as loss and if the cost price is less than the selling price then it is called as profit or gain
Here, we can see that the selling price of milk is greater than the cost price.
So, we can say that the milkman has a gain.
Let us assume that the gain percentage of milkman as \['x'\]
We know that the formula for gain percentage is given as
\[\text{gain percentage}=\dfrac{S.P-C.P}{C.P}\times 100\]
Now, by using the above formula we get the gain percentage as
\[\begin{align}
  & \Rightarrow x=\dfrac{50-40}{40}\times 100 \\
 & \Rightarrow x=\dfrac{10\times 100}{40} \\
 & \Rightarrow x=25\% \\
\end{align}\]

Therefore the gain percentage of the milkman is 25%.

Note: We can decide whether the person has loss or gain from the percentage also.
We take the formula for the percentage as
\[\text{Percentage}=\dfrac{S.P-C.P}{C.P}\times 100\]
If the percentage we get is positive then we can say that he has gain and if the percentage is negative then we can say that he has loss.
Let us assume that the percentage of milkman as \['x'\]
Now by using the above formula to given question we get
\[\begin{align}
  & \Rightarrow x=\dfrac{50-40}{40}\times 100 \\
 & \Rightarrow x=25\% \\
\end{align}\]
Here, we can see that the percentage is positive so we can conclude that the milkman has a gain of 25%.