Question

The sold price of $12$ eggs is equal to cost price of $16$ eggs. Find the profit percentage

Answer 1

Let selling price of $12$ eggs $=\mathrm{X}$

Then the cost price of $16$ eggs $=\mathrm{X}$

The selling price of $1\mathrm{egg}=\frac{\mathrm{X}}{12}$

Therefore, the cost price of $1\mathrm{egg}=\frac{\mathrm{X}}{16}$

We know that selling price > cost price

Therefore, the profit = Selling price – Cost price

$=\frac{\mathrm{X}}{12}–\frac{\mathrm{X}}{16}=\frac{\mathrm{X}}{48}$

$\mathrm{Profit}\%=\left(\frac{\mathrm{Profit}}{\mathrm{CP}}\right)\mathrm{x}100\%$

$$\begin{gathered} =\frac{{\displaystyle \frac{\mathrm{X}}{48}}}{{\displaystyle \frac{\mathrm{X}}{16}}}\times 100 \\ =\frac{16}{48}\times 100 \\ =\frac{100}{3} \\ =33\frac{1}{3}\% \end{gathered}$$

Hence, the profit percentage is $33\frac{1}{3}\%$