Radha marks her goods 25% above the cost price. She sells 35% of goods at the marked price, 40% at 15% discount and the remaining at 20% discount. What is her overall percentage gain?

Solution (By Examveda Team)

\[\begin{array}{*{20}{c}} {{\text{Cost price}}}&{}&{{\text{Marked price}}} \\ {400}&:&{500} \\ {{\text{Number of goods}}}& \to &{35:40:25 = 7:8:5} \\ {}&{}&\begin{gathered} {\text{Selling price}} \hfill \\ \, \downarrow \hfill \\ \end{gathered} \\ {7 \times 500}& = &{3500} \\ {8 \times 425}& = &{2000} \\ {5 \times 400}& = &{2000} \\ {{\text{Total selling price}}}& = &{{\text{Rs}}{\text{. }}8900} \\ {{\text{Cost price}}}& = &{400\left( {7 + 8 + 5} \right)} \\ {}& = &{{\text{Rs}}{\text{. }}8000} \\ {{\text{Profit}}}& = &{{\text{Selling price}} - {\text{Cost price}}} \\ {}& = &{8900 - 8000 = 900} \\ {{\text{Profit}}\,\% }&{ = \frac{{900}}{{8000}} \times 100}&{ = 11.25\% } \end{array}\]