The selling price of 12 pens is equal to the cost price of 15 pens. Find the gain per cent.

Given: Selling price of 12 pens is equal to the cost price of 15 pens.

To find: Here we have to find the gain percentage.

Solution:

Let the cost price of 15 pens = a

So,

$Selling\ price\ of\ 12\ pens\ =\ a$

$Selling\ price\ of\ 1\ pen\ =\ \frac{a}{12}$

$Selling\ price\ of\ 15\ pens\ =\ \frac{15a}{12}$

Now,

$Profit\ =\ SP\ of\ 15\ pens\ -\ CP\ of\ 15\ pens$

$Profit\ =\ \frac{15a}{12} \ -\ a$

$Profit\ =\ \frac{15a\ -\ 12a}{12}$

$Profit\ =\ \frac{3a}{12}$

$Profit\ =\ \frac{a}{4}$

Therefore profit % is as below,

$Profit\ \%\ =\ \frac{Profit}{CP} \ \times \ 100\ \ \%$

$Profit\ \%\ =\ \frac{\frac{a}{4}}{a} \ \times \ 100\ \ \%$

$Profit\ \%\ =\ \frac{1}{4} \ \times \ 100\ \ \%$

$\mathbf{Profit\ \%\ =\ 25\ \%}$

So, the answer is 25%.