A fruit vendor buys oranges at the rate of 5 for Rs.40 and sells them at Rs.9 per orange. Find his gain percent.

Hint: Percentage gain means to express the profit or the gain in the form of percentages. This way makes it easier and faster for a person to understand the variables or the vitals of a business transaction.
\[Gain{\text{ }}\% {\text{ }} = {\text{ }}\left( {\dfrac{{Gain{\text{ }}}}{{\operatorname{Cos} t\Pr ice}}} \right){\text{ }}*{\text{ }}100\]

Complete step-by-step answer:
To tackle this problem first we calculate the cost price and selling price of one orange. The difference in cost and selling price of one orange in the gain. We can see that the fruit vendor has sold the oranges at a better price, so this is his gain. To work out the increase as a percentage it is now necessary to divide the increase by the original price of the orange i.e the cost price.
We will first find the cost price of 1 orange:
No of oranges bought by the fruit vendor = 5
Total cost price of oranges = Rs. 40
Cost Price for single orange = $\dfrac{{Total\cos t\;price}}{{No\;of\;oranges}} = \dfrac{{40}}{5} = Rs.8$
Now we will find the selling price of 1 orange:
Selling Price of oranges sold by the fruit vendor = Rs. 9
Gain = Selling Price – Cost Price = 9 – 8 = Rs. 1
Now we will find the gain percentage:
For finding the gain percentage, we will use the formula of Gain % as mentioned in the hint.
\[
  Gain{\text{ }}\% {\text{ }} = {\text{ }}\left( {\dfrac{{Gain{\text{ }}}}{{\operatorname{Cos} t\Pr ice}}} \right){\text{ }}{\rm X}{\text{ }}100 \\
   \Rightarrow Gain{\text{ }}\% {\text{ }} = \left( {\dfrac{1}{8}} \right){\rm X}100 \\
   \Rightarrow Gain{\text{ }}\% {\text{ }} = 12.5\% \\
 \]

The gain earned by the fruit vendor in selling the oranges is 12.5%

Note: Profit percentage and loss percentage are always calculated on cost price unless otherwise stated. While the percentage increase is important in mathematics, it is also useful in science, such as calculating percent increase in mass of a chemical element in a compound.