Siyaram has 100 Kg apples, he sells a part of it at 8% profit and rest of it at 18% profit. The overall profit he earns is 14%. The quantity he sold at 18% profit is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 60 Kg
All the apples cost the same per kg, so the overall profit percentage is the weighted average of the two rates, weighted by quantity. Let x kg be sold at 18% profit; then \(100 - x\) kg are sold at 8% profit.
\(8(100 - x) + 18x = 14 \times 100\)
\(800 + 10x = 1400\)
\(10x = 600\)
\(x = 60\)
So 60 kg were sold at 18% profit.
Shortcut: By the rule of alligation, quantity at 8% : quantity at 18% = \((18 - 14) : (14 - 8) = 4 : 6 = 2 : 3\). So the 18% part is \(\frac{3}{5} \times 100 = 60\) kg.
CBSE Applied Mathematics (Class XII):
Alligation and Mixture
