Question

The cost price of an article is Rs. 2400 which is 20% below the marked price. If it is sold at a discount of 16% on the marked price, find: 1. marked price. 2. selling price 3. the profit percentage.

Answer 1

$$\begin{gathered} 1. \\ \mathrm{Suppose}\mathrm{the}\mathrm{marked}\mathrm{price}\mathrm{of}\mathrm{an}\mathrm{article}\mathrm{be}\mathrm{Rs}\mathrm{x} \\ \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the}\mathrm{cost}\mathrm{price}\mathrm{is}\mathrm{Rs}2400\mathrm{which}\mathrm{is}20\%\mathrm{below}\mathrm{the}\mathrm{marked}\mathrm{price}. \\ \mathrm{This}\mathrm{implies}\mathrm{that}, \\ \mathrm{x}-20\%\mathrm{of}\mathrm{x}=2400 \\ \mathrm{x}-\frac{20}{100}\times \mathrm{x}=2400 \\ \mathrm{x}-\frac{20\mathrm{x}}{100}=2400 \\ \frac{100\mathrm{x}-20\mathrm{x}}{100}=2400 \\ \frac{80\mathrm{x}}{100}=2400 \\ 80\mathrm{x}=240000 \\ \mathrm{x}=\frac{240000}{80} \\ \mathrm{x}=3000 \\ \mathrm{So}\mathrm{the}\mathbf{marked}\mathbf{}\mathbf{price}\mathbf{}\mathbf{is}\mathbf{}\mathbf{Rs}\mathbf{}\mathbf{3000} \\ 2. \\ \mathrm{The}\mathrm{article}\mathrm{is}\mathrm{sold}\mathrm{at}\mathrm{a}\mathrm{discount}\mathrm{of}16\%\mathrm{on}\mathrm{the}\mathrm{marked}\mathrm{price}. \\ \mathrm{So}\mathrm{the}\mathbf{selling}\mathbf{}\mathbf{price}\mathrm{is}\mathrm{given}\mathrm{by}, \\ \mathrm{Selling}\mathrm{price}=3000-16\%\mathrm{of}3000 \\ =3000-\frac{16}{100}\times 3000 \\ =3000-16\times 30 \\ =3000-480 \\ =2520 \\ 3. \\ \mathrm{The}\mathrm{profit}\mathrm{percent}\mathrm{is}\mathrm{given}\mathrm{by}, \\ \mathrm{profit}\%=\frac{\mathrm{profit}}{\mathrm{cost}\mathrm{price}}\times 100 \\ \mathrm{Note}\mathrm{that}, \\ \mathrm{profit}=\mathrm{Selling}\mathrm{price}-\mathrm{cost}\mathrm{price} \\ =2520-2400 \\ =120 \\ \mathrm{So}\mathrm{the}\mathrm{required}\mathrm{profit}\%\mathrm{is}, \\ \mathbf{profit}\mathbf{}\mathbf{\%}=\frac{120}{2400}\times 100 \\ =\frac{12000}{2400} \\ =5\% \end{gathered}$$