Question

A merchant incurred a loss of 5% by selling a book for 25.65. If he sells it for 31.05, find his gain percent or loss percent.

Answer 1

loss%$=\frac{loss}{Cost price}×100$

$5 = \frac{x - 25.65}{x} × 100$

$\frac{5}{100} = [ 1 - (\frac{25.65}{x}]$

$\frac{1}{20} = [1 - (\frac{25.65}{x}]$

$\frac{25.65}{x} = [1 - (\frac{1}{20}]$

$\frac{25.65}{x} = \frac{19}{20}$

$\frac{2565}{100x} = \frac{19}{20}$

$\frac{2565}{5x} = 19$

$\frac{513}{19} = x$

$x = 27$

$=> Cost price of book =27rupees$

When the merchant sells this book for 31.05 rupees , then

profit$= 31.05 - 27 = 4.05$

Now ,

profit %$= \frac{profit}{C.P.}×100$

$= \frac{4.05}{27}×100$

$= \frac{405}{27}$

$= 15%$