The selling price of 16 books is equal to the cost price of 12 books. Find the loss or gain percentage.

Correct option is A

Given:

The selling price of 16 books equals the cost price of 12 books.

Formula Used:

Loss = CP - SP 

​$$\text{Loss Percentage}= \frac{Loss}{\text{Cost Price}}\times100$$ ​

Solution:

Let:

The cost price of one book be C.

The selling price of one book be S. 

We are given that the selling price of 16 books is equal to the cost price of 12 books:

16S = 12C 

Simplify the equation to express the relationship between the selling price $S$ and the cost price $C$:

$$\frac{C}{S} = \frac{16}{12} = \frac{4}{3}$$ 

It means if cost price is 4 then selling price is 3 Since the selling price is less than the cost price, we know that there is a loss.

Loss = CP - SP = 4 - 3 = 1 

​$$\text{Loss Percentage}= \frac{Loss}{\text{Cost Price}}\times100$$​​

Loss percentage = $$\frac{1}{4}\times100$$ = 25%

Thus The loss percentage is 25%. ​