Question

By selling 100 Diwali cards, a shopkeeper gains an S.P. of 40 cards. Find the gain percent.

Answer 1

Hint: At first we will assume the selling price of a Diwali card to be x, using this we’ll find the selling price of 100 Diwali cards and the profit earned from it. Now we’ll calculate the cost price using the selling price and profit.
Now we get all the required values to find the gain percent, so we’ll find the gain percent as asked.

Complete step-by-step answer:
Given data: Number of Diwali cards sold $ = 100$
Profit $ = $ S.P. of 40 cards
Let the selling price of a Diwali card be x
Therefore the total selling price if the 100 Diwali cards $ = 100x$
And the profit $ = 40x$
We know that the cost price $ = $ selling price $ - $ profit
Similarly, cost price of the 100 Diwali cards $ = $ selling price of the 100 Diwali cards $ - $ profit on the 100 Diwali cards
i.e. cost price $ = 100x - 40x$
 $ = 60x$
We know that the gain percent formula is given by $\dfrac{{profit}}{{C.P.}} \times 100$
Therefore the gain percent on 100 Diwali cards $ = \dfrac{{40x}}{{60x}} \times 100$
 $ = \dfrac{{200}}{3}$
On solving we get,
 $ = 66.\bar 6\% $
The required gain percent is $66.\bar 6\% $.

Note: Most of the students while writing the formula for gain percent, they take the selling price in the denominator which is not correct. It should be the cost price that is the main reference, so while writing formulas like this we should remember all the terms to apply them correctly.