A shopkeeper has 300 Kg millet, a part of which he sells at 10% profit. The remaining quantity of millet was of poor quality, and he sold it at a 5% loss. In the whole transaction, he made a profit of 7%. The quantity of the millet sold at 5% loss is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 60 Kg
Let x kg be sold at a 5% loss, so (300 − x) kg is sold at a 10% profit. Let the cost price be Rs. 1 per kg. The total profit on the two parts must equal 7% of the total cost:
\(0.10(300 - x) - 0.05x = 0.07 \times 300\)
\(30 - 0.15x = 21\)
\(0.15x = 9,\quad x = 60\)
So 60 kg was sold at a 5% loss.
Shortcut: By alligation, the quantities are in the ratio of the opposite differences from the mean 7%:
\(\text{loss part} : \text{profit part} = (10 - 7) : (7 - (-5)) = 3 : 12 = 1 : 4\)
\( \displaystyle \text{loss part} = \frac{1}{5} \times 300 = 60 \text{ kg} \)