A retailer has 900 kg of wheat, a part of which he sells at 10% loss and the remaining at a profit of 8%. Overall, he makes a profit of 6%, the quantity sold at profit is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 800 kg
Let the cost price be Rs. 1 per kg, and let x kg be sold at a loss, so \(900 - x\) kg are sold at a profit.
The total profit must be 6% of the cost of all 900 kg:
\(-0.10x + 0.08(900 - x) = 0.06 \times 900\)
\(-0.10x + 72 - 0.08x = 54\)
\(0.18x = 18\)
\(x = 100\)
So the quantity sold at a profit is \(900 - 100 = 800\) kg.
Shortcut: By the rule of alligation, with −10% and 8% mixed to give 6%:
loss part : profit part \(= (8 - 6) : (6 - (-10)) = 2 : 16 = 1 : 8\)
\( \displaystyle \text{profit part} = \frac{8}{9} \times 900 = 800 \text{ kg} \)