A shopkeeper has 180 kg of cumin seeds, a part of which he sells at 12% profit. The remaining quantity of cumin seeds is of low quality and that is why he sold it at 6% loss. Overall, he made a profit of 8%. The quantity of cumin seeds sold at 6% loss is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 40 kg
The whole stock is taken to have the same cost price per kg, so the profit percentages can be combined by quantity.
Let x kg be sold at 6% loss, so (180 − x) kg is sold at 12% profit. The overall profit is 8% of the whole:
\( \displaystyle 12(180-x)-6x=8\times 180 \)
\( \displaystyle 2160-18x=1440 \)
\( \displaystyle 18x=720 \)
\( \displaystyle x=40 \)
So 40 kg was sold at 6% loss.
Shortcut: By the rule of alligation, with 12% profit, 6% loss (−6%) and mean 8%:
\( \displaystyle \text{Profit part}:\text{Loss part}=(8-(-6)):(12-8) \)
\( \displaystyle \text{Profit part}:\text{Loss part}=14:4=7:2 \)
\( \displaystyle \text{Loss part}=\frac{2}{9}\times 180=40\text{ kg} \)
Why the other options are incorrect
Option (1) 140 kg — Incorrect. 140 kg (= 180 − 40) is the quantity sold at 12% profit, not at 6% loss.
Option (2) 60 kg — Incorrect. With 60 kg at a loss, the overall profit is \( \frac{12\times 120-6\times 60}{180}=6\% \), not 8%.
Option (4) 80 kg — Incorrect. With 80 kg at a loss, the overall profit is \( \frac{12\times 100-6\times 80}{180}=4\% \), not 8%.
CBSE Applied Mathematics (Class XII):
Alligation and Mixture
