Question

By selling 8 dozen pencils, a shopkeeper gains the selling price of one dozen pencils. Find his gain per cent.

Answer 1

Let the CP of one pencil be Rs. x.
Therefore, the CP of 96 pencils will be Rs. 96x.
Let SP of one pencil be Rs. y.
​∴ SP of 96 pencils = Rs. 96y
Gain= SP of one dozen pencil = Rs.12y (given)

Gain = SP - CP

$$\begin{gathered} \Rightarrow 12y=96y-96x \\ \Rightarrow 96x=96y-12y \\ \Rightarrow 96x=84y \\ \Rightarrow x=\frac{84y}{96} \end{gathered}$$

$$\begin{gathered} \mathrm{Gain}\%=\left(\frac{\mathrm{Gain}}{\mathrm{CP}}\times 100\right)\% \\ =\left(\frac{12y}{96x}\times 100\right)\% \\ =\left(\frac{12y\times 96}{96\times 84y}\times 100\right)\% \\ =14.28\% \end{gathered}$$