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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%.