Question

A grocer purchased 200 kg of rice at Rs 25 per kg. He sold 80 kg of it at a gain of 10% and 40 kg at a loss of 4%. At what rate per kg should he sell the remainder to gain 8% on his total investment?

Answer 1

CP of 1 kg of rice = Rs 25
C.P of 200 kg rice= $\mathrm{Rs}(200\times 25)=\mathrm{Rs}5000$
CP of 80 kg of rice=$\mathrm{Rs}(25\times 80)=\mathrm{Rs}2000$

CP of 40 kg of rice =$\mathrm{Rs}(25\times 40)=\mathrm{Rs}1000$

$$\begin{gathered} \mathrm{SP}\mathrm{of}80\mathrm{kg}\mathrm{of}\mathrm{rice}=\frac{100+\mathrm{gain}\%}{100}\times \mathrm{CP} \\ =\mathrm{Rs}\frac{110}{100}\times 2000 \\ =\mathrm{Rs}2200 \end{gathered}$$

$$\begin{gathered} \mathrm{SP}\mathrm{of}40\mathrm{kg}\mathrm{rice}=\frac{100-\mathrm{loss}\%}{100}\times \mathrm{CP} \\ =\mathrm{Rs}\frac{96}{100}\times 1000 \\ =\mathrm{Rs}960 \end{gathered}$$

$$\begin{gathered} \mathrm{SP}\mathrm{of}200\mathrm{kg}\mathrm{rice}=\frac{100+\mathrm{gain}\%}{100}\times \mathrm{CP} \\ =\mathrm{Rs}\frac{108}{100}\times 5000 \\ =\mathrm{Rs}5400 \end{gathered}$$

Remaining quantity of rice = (200 − 80 + 40) kg = 80 kg

​SP of the remaining rice (80 kg) = Rs (5400 − 2200 − 960)
= Rs 2240

$\therefore \mathrm{Rate}\mathrm{per}\mathrm{kg}=\mathrm{Rs}\frac{2240}{80}=\mathrm{Rs}28$