Question

The selling price of 18 books is equal to the cost price of 21 books. Find the gain or loss percent.

Answer 1

Hint: According to the question, we are being asked to find the gain or loss percent when the selling price of 18 books is equal to the cost price of 21 books. Now, we know that it is a gain when the selling price is greater than the cost price and it is a loss when the cost price is greater than the selling price. Now, we know that
$\text{Gain}\%=\dfrac{\text{gain}\times 100}{CP} \\ $
$ \text{Loss}\%=\dfrac{\text{loss}\times 100}{CP} \\ $

Complete step by step solution:
As per the given question we need to find the gain or loss percent where we are provided with the information that the cost price of 21 books is equal to the selling price of 18 books. Also, we know that
Gain%=$\dfrac{gain\times 100}{CP} $
Loss%=$\dfrac{loss\times 100}{CP} $
Let us assume that the cost price of one article is 1Re.
Now, the selling price of 18 books is 21Rs.
Therefore, selling price of one book is $\dfrac{21}{18}=\dfrac{7}{6}=1.167$
Clearly, we can see that selling price is greater than cost price therefore, it is a gain.
Now,
$\text{Gain}=\dfrac{7}{6}-1 $
$\Rightarrow \text{Gain}=\dfrac{1}{6} $
Now, we are asked to find the gain percent which is given by the formula given above. Now substituting the values in it we get,
$ \text{Gain}\%=\dfrac{1}{6}\times 100 $
$ \Rightarrow \text{Gain}\%=\dfrac{50}{3} $
which can be written as $Gain\%=16\dfrac{2}{3}\%$
Therefore, the gain percent of the given information is $Gain\%=16\dfrac{2}{3}\%$

Note: We should start this type of problems basically by assuming some variable say and then using the information given in the question we need to find the relation between the selling price and cost price and then proceed with the question to find the loss or gain.