Given,
Selling price = 405, Profit = 12.5%
let cost price be $$x$$ and 12.5% profit can be written as 100 + 12.5 = $$\frac{112.5}{100}$$
$${x}\times\frac{112.5}{100}$$ = 405
$$x$$ = $$\frac{{405}\times{100}}{112.5}$$
$$x$$ = $$\frac{{405}\times{1000}}{1125}$$
$$x$$ = 360
profit earned = 405 - 360
                    = 45
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