A shopkeeper bought 40 pieces of an article at a rate of Rs. 50 per item. He sold 35 pieces with 20% profit. The remaining 5 pieces were found to be damaged and he sold them with 10% loss. Find his overall profit percentage.

Solution(By Examveda Team)

$$\eqalign{ & {\text{Total cost price of 40 article}} = {\text{Rs}}{\text{. }}2000 \cr & {\text{Sale price of 35 article}} \cr & = 35 \times 50 \times \frac{{120}}{{100}} = {\text{Rs}}{\text{. }}2100 \cr & {\text{Sale price of 5 article}} \cr & = 5 \times 50 \times \frac{{90}}{{100}} = {\text{Rs}}{\text{. }}225 \cr & \therefore {\text{Total sale price of 40 article}} \cr & = 2100 + 225 = {\text{Rs}}{\text{. }}2325 \cr & \therefore {\text{Overall profit}} = 2325 - 2000 = {\text{Rs}}{\text{. }}325 \cr & \therefore {\text{Profit }}\% = \frac{{325}}{{2000}} \times 100 = 16.25\% \cr & \cr & {\bf{Alternate}}\,{\bf{solution}} \cr} $$
\[\begin{array}{*{20}{c}} {{\text{Article}} \to }&{35}&:&5 \\ {}&7&:&1 \\ {}&{20\% }&{}&{ - 10\% } \end{array}\]
$$\eqalign{ & {\text{Overall profit }}\% \cr & = \frac{{7 \times 20\% - 1 \times 10\% }}{{7 + 1}} \cr & = \frac{{140\% - 10\% }}{8} \cr & = \frac{{130}}{8}\% \cr & = 16.25\% \cr} $$