Question

What is the profit percent if the cost price of $50$oranges is equal to the selling price of $40$oranges?
A). $12.5\% $
B). $25\% $
C). $35\% $
D). $40\% $

Answer 1

Hint: In this problem, we want to find the profit percentage. By understanding the data we can solve the problem easily. And also we are going to use the formula for the profit percent. Profit in mathematics is defined as the gain of the product. Sell the product for more than the cost price, we can make a profit.
Formula used:
$profit{\kern 1pt} {\kern 1pt} {\kern 1pt} \% = \dfrac{{100 \times profit}}{{C.P}}$

Complete step-by-step solution:
In this problem, we are going to find the profit percentage of the given problem.
First, we have to know what the data given in the problem is.
Let us take, the cost of one orange is equal to one rupee.
Therefore the cost price of the fifty oranges is fifty rupees.
The cost price of forty oranges is forty rupees.
But the customer bought forty oranges for fifty rupees.
We can write this as,
The cost price of fifty oranges = the selling price of forty oranges.
That is forty oranges are equal to fifty rupees.
Forty oranges selling price is equal to fifty rupees.
Let us take, $40 \times S.P = 50$
Now selling price is, $S.P = \dfrac{{50}}{{40}}$
On solving,
$S.P = 1.25$
Therefore the selling price of each orange is $1.25$rupees.
Therefore, twenty-paise profit on each orange.
Therefore profit for forty oranges is $ = 0.25 \times 40$
Now we get,
Profit is $10$ rupees.
Now we are going to find the profit percent.
Apply the values in the formula, we get
 Profit percent$\text{Profit} \% = \dfrac{{100 \times 10}}{{40}}$
Now we get, $\text{Profit} \% = 25\% $
Therefore the answer is option B.

Note: Profit is defined as the additional income gained from selling the product. When the selling price is more than the cost price we get the gain. Profit is equal to subtract the cost price from the selling price. And also it is the positive income.