A cloth merchant sold half of his cloth at 20% profit, half of the remaining cloth at 20% loss and the rest was sold at its cost price. In the total transaction, his gain or loss will be = ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let}}\,{\text{CP}}\,{\text{of}}\,{\text{whole}}\,{\text{be}}\,{\text{Rs}}{\text{.}}\,x \cr & {\text{CP}}\,{\text{of}}\,\frac{1}{2}\,{\text{stock}} = {\text{Rs}}{\text{.}}\,\frac{x}{2} \cr & {\text{CP}}\,{\text{of}}\,\frac{1}{4}\,{\text{stock}} = {\text{Rs}}{\text{.}}\,\frac{x}{4} \cr} $$
$${\text{Total }}\,{\text{SP}}$$
$$ = \,\left[ {\left( {120\% \,{\text{of}}\,\frac{x}{2}} \right) + \left( {80\% \,{\text{of}}\,\frac{x}{4}} \right) + \frac{x}{4}} \right]$$
$$\eqalign{ & = \left( {\frac{{3x}}{5} + \frac{x}{5} + \frac{x}{4}} \right) \cr & = {\text{Rs}}{\text{.}}\,\frac{{21x}}{{20}} \cr & {\text{Gain}} = {\text{Rs}}{\text{.}}\,\left( {\frac{{21x}}{{20}} - x} \right) = {\text{Rs}}{\text{.}}\,\frac{x}{{20}} \cr & \therefore {\text{Gain}}\% = \left( {\frac{x}{{20}} \times \frac{1}{x} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5\% \cr} $$