Question

By selling 100 mangoes, a fruit seller gains the S.P of 20 mangoes. Find his gain %.

Answer 1

Hint: Here, first of all, take the S.P of each mango as Rs. x. From this find the S.P of 20 mangoes and equate it to the gain on 100 mangoes. From this find the C.P of 100 mangoes. Then find the gain % by using the formula, \[\text{Gain }\%\text{ }=\dfrac{\text{Gain}}{\text{C}\text{.P}}\times 100\].

Complete step-by-step answer:
Here we are given that by selling the 100 mangoes, a fruit seller gains the S.P of 20 mangoes. We have to find the gain %. Before proceeding with this question, we must know the following terms:
Cost Price (C.P): This is the price at which the article is purchased by the shopkeeper/seller.
Selling Price (S.P): This is the price at which the article is sold by the shopkeeper/seller.
Profit or Gain: If the selling price is more than the cost price, the difference between them is the profit/gain incurred.
The formula for gain and gain % is as follows:
Profit/Gain = S.P – C.P
\[\text{Gain }\%\text{ }=\dfrac{\text{Gain}}{\text{C}\text{.P}}\times 100\].

Now let us consider our question. Let us take the selling price (S.P) of each mango = Rs. x.
So, we get the selling price (S.P) of 20 mangoes = Rs. 20x.
Also, we get the selling price (S.P) of 100 mangoes = Rs. 100x.
We are given that by selling 100 mangoes, fruit seller gains S.P of 20 mangoes, so we get,
Gain on selling 100 mangoes = S.P of 20 mangoes.
By substituting the value of S.P of 20 mangoes = 20x, we get, Gain on selling 100 mangoes = Rs. 20x.
Now, we know that Gain = S.P – C.P. So, we get (S.P of 100 mangoes) – (C.P of 100 mangoes) = 20x.
By substituting the value of S.P of 100 mangoes = 100x, we get, 100x – (C.P of 100 mangoes) = 20x.
So, we get 100x – (C.P of 100 mangoes) = 20x.
So, we get, (C.P of 100 mangoes) = 100 – 20x = Rs. 80x.
So, for 100 mangoes, we get,
C.P = 80x
S.P = 100x
Gain = 20x
Now, we know that,
\[\text{Gain }\%\text{ }=\dfrac{\text{Gain}}{\text{C}\text{.P}}\times 100\].
By substituting the value of Gain and C.P, we get,
\[\text{Gain }\%\text{ }=\dfrac{20x}{80x}\times 100\]
\[=\dfrac{1}{4}\times 100\]
= 25 %
So, we get the gain % on selling 100 mangoes as 25 %.

Note: Here, some students make this mistake of taking the S.P of 100 mangoes as x which unnecessarily increases the steps of questions, and students get confused due to various fractional values. So, it is better to consider the S.P of each mango as x. Also, in this question, by reading the question, some students think that gain is given for selling 20 mangoes but gain is given for selling 100 mangoes which is equal to S.P of 20 mangoes. So, students should properly interpret the question first and then only proceed to solve it.