Question

When Vijay sells $12$ pens, he gains the selling price of $2$ pens. Calculate his gain percentage.

Answer 1

Hint: As we know that the above given question is a word problem. A problem is a mathematical question written as one sentence or more describing a real life scenario where that problem needs to be solved by the way of mathematical calculation.

Formula used:
We can solve the given problem by applying the formula of gain percent i.e. $Gain\% = \dfrac{{SP - CP}}{{CP}} \times 100$, where SP is the selling price and CP is the cost price.

Complete step by step answer:
We need to first understand the requirement of the question which is the gain or profit percent.Let us assume that the selling price of one pen is $Rs\,1$.
So the selling price of $12$ pens $ = 12 \times 1 = Rs\,12$.
According to the question we are given that He gains a selling price of two pens i.e. $1 \times 2 = Rs\,2$.

Thus his profit amount is $Rs\,\,2$. Now we know the formula that,
$\text{Profit or Gain = Selling Price- Cost Price}$
We have a Selling Price$(SP) = Rs\,\,12$ , Cost price$(CP) = Rs\,\,10$ and Profit$ = Rs\,2$.
By putting this in the formula we have, $2 = 12 - CP$, now we solve them $CP = 12 - 2 = 10$.
Since the formula of gain% is $Gain\% = \dfrac{{SP - CP}}{{CP}} \times 100$,
by substituting all the values we can write,
$gain\% = \dfrac{{12 - 10}}{{10}} \times 100$
On further solving we have,
$\therefore gain\% \dfrac{2}{{10}} \times 100 = 20\% $.

Hence the required gain percent received by Vijay is $20\% $.

Note:We should always be careful what the question is asking and also remember all the formulas. If Cost price is more than Selling price, then we face the loss and the formula for Loss% is $Loss\% = \dfrac{{CP - SP}}{{CP}} \times 100$. Based on the requirement and by observing all the necessary information that is already available in the question we gather the information and then create an equation or by unitary method whichever is applicable, then we solve the problem and then verify the answer by putting the value in the problem and see whether we get the same answer or not.