Question

A shopkeeper earns a profit of Rs 2 by selling a pen and incurs a loss of 50 paise per pencil and loss of 15 paise per eraser while selling pencils and erasers of old stock. On a particular day, he earns a profit of Rs 10. If he sold 10 pens and the number of pencils and erasers he sold are in the ratio 7: 10, then find the number of pencils and erasers he sold on that day.

Answer 1

Dear student
$$\begin{gathered} \mathrm{Profit}\mathrm{earned}\mathrm{by}\mathrm{selling}\mathrm{a}\mathrm{pen}=\mathrm{Rs}2 \\ \mathrm{Profit}\mathrm{earned}\mathrm{by}\mathrm{selling}10\mathrm{pens}=\mathrm{Rs}2\times 10=\mathrm{Rs}20 \\ \mathrm{Overall}\mathrm{profit}=\mathrm{Rs}10 \\ \mathrm{Loss}\mathrm{incurred}=\mathrm{profit}\mathrm{earned}\mathrm{on}\mathrm{pens}-\mathrm{Overall}\mathrm{profit}=\mathrm{Rs}\left(20-10\right)=-\mathrm{Rs}10 \\ \mathrm{Loss}\mathrm{incurred}\mathrm{by}\mathrm{selling}\mathrm{one}\mathrm{pencil}=\mathrm{Rs}0.5 \\ \mathrm{Loss}\mathrm{incurred}\mathrm{by}\mathrm{selling}\mathrm{on}\mathrm{eraser}=\mathrm{Rs}0.15 \\ \mathrm{Let}\mathrm{the}\mathrm{common}\mathrm{ratio}\mathrm{be}\mathrm{x} \\ \mathrm{So},\mathrm{Total}\mathrm{loss}\mathrm{on}\mathrm{pencil}\mathrm{and}\mathrm{eraser}=7\mathrm{x}\left(0.5\right)+10\mathrm{x}\left(0.15\right) \\ \Rightarrow 10=3.5\mathrm{x}+1.5\mathrm{x} \\ \Rightarrow 10=5\mathrm{x} \\ \Rightarrow \mathrm{x}=2 \\ \mathrm{Therefore},\mathrm{number}\mathrm{of}\mathrm{pencils}\mathrm{sold}\mathrm{that}\mathrm{day}=7\times 2=14 \\ \mathrm{and}\mathrm{number}\mathrm{of}\mathrm{erasers}\mathrm{sold}\mathrm{that}\mathrm{day}=10\times 2=20 \end{gathered}$$
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