A grocer bought 200 kg of rice at Rs. 200/kg. He sold 80 kg at gain of 10 % and sold 40 kg at loss of 4%. At what percent should he sell the remaining rice to gain 8% on total transaction?

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Solution

Cost price of 1 kg of rice = Rs.25
Then, cost price of 200 kg of rice = $25 \times 200$ = Rs.5000
Cost price of 80 kg of rice = $25 \times 80$ = Rs.2000
Gain = 10%
So selling price of 80 kg of rice = $2000 + 2000 \times \frac{10}{100} = 2000 + 200$ = Rs.2200
And cost price of 40 kg of rice = $25 \times 40$ = Rs.1000
Loss = 4%
So, selling price of 40 kg of rice = $1000 - 1000 \times \frac{4}{100}$ = Rs.960
So selling price of (80 kg + 40 kg) ie. 120 kg of rice = Rs.2200 + Rs.960 = Rs.3160
Then the remaining rice to be sold = 200 kg - 120 kg = 80 kg
Selling price of 200 kg of rice to have a gain of 8% on whole = $5000 + 5000 \times \frac{8}{100}$ = Rs.5400
This means selling price of remaining 80 kg of rice should be = Rs.5400 - Rs.3160 = Rs.2240
And cost price of remaining 80 kg of rice = Rs.2000
So net gain = Rs.2240 - Rs.2000 = Rs.240
Therefore gain percentage of remaining 80 kg of riceshould be = $\frac{net gain \times 100}{Cost price} = \frac{240 \times 100}{2000} = 12 %$

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