Question

Rao bought goods worth Rs.800 .He sold 1/4 of it at a gain of 12% and 1/2of it at a loss of 10% . At what profit percentage he should sell the remaining goods so as to gain 8% on the whole transaction?

Answer 1

Cost price of goods = Rs.800
Cost price of $\frac{1}{4}$ of goods = $\frac{1}{4}\times 800$ = Rs.200
Gain percentage = 12%
So, selling price of $\frac{1}{4}$ of goods = $200+200\times \frac{12}{100}$ = Rs.224
And cost price of $\frac{1}{2}$ of goods = $\frac{1}{2}\times 800$ = Rs.400
Loss percentage = 10%
So, selling price of $\frac{1}{2}$ of goods = $400-400\times \frac{10}{100}$ = Rs.360
So selling price of $\left(\frac{1}{2}+\frac{1}{4}\right)\mathrm{i}.\mathrm{e}.\frac{3}{4}$ of goods = Rs.224 + Rs.360 = Rs.584
And cost price of remaining goods = Rs.800 - (Rs.400 + Rs.200) = Rs.200
To have a gain of 8% on whole goods, the selling price of whole goods = $800+800\times \frac{8}{100}$ = Rs.864
So, Rao should sell the remaining goods at price = Rs.864 - Rs.584 = Rs.280
Means to have profit of 8%, net profit on remaining goods = Rs.280 - Rs.200 = Rs.80
Therefore required profit percentage = $\frac{\mathrm{net}\mathrm{profit}\times 100}{\mathrm{cost}\mathrm{price}}=\frac{80\times 100}{200}=40\%$