Two-thirds of the consignment was sold at a profit of 8% and the remainder at a loss of 4%. If the total profit was ₹500, find the value of the consignment?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → ₹ 12500
The profit on each part is a percentage of that part’s value, so the total profit is found as a percentage of the whole consignment and then compared with ₹500.
Assuming the value of the consignment to be ₹\(x\):
Profit on two-thirds at 8%: \(\displaystyle\frac{2x}{3}\times\frac{8}{100}=\frac{16x}{300}\)
Loss on the remaining one-third at 4%: \(\displaystyle\frac{x}{3}\times\frac{4}{100}=\frac{4x}{300}\)
Net profit \(\displaystyle=\frac{16x-4x}{300}=\frac{12x}{300}=\frac{x}{25}\), that is, 4% of the value
\(\displaystyle\frac{x}{25}=500\), so \(x=\) ₹12,500
Shortcut:
The rate on the whole consignment is the weighted average of the two rates: \(\displaystyle\frac{2\times8+1\times(-4)}{3}=4\%\) profit
4% of the value is ₹500, so the value is \(500\times25=\) ₹12,500