A man bought 400 m of fabric @ Rs. 60 per metre. He sold 50% of it at a profit of 4%. At what percent should he sell the remaining to gain 12% on the whole transaction?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 20%
The gain on the whole transaction is the total selling price minus the total cost, so the price needed for the second half is what is left of the target after the first half has been sold.
The target (12% gain on the total cost):
Total cost \(=400\times60=\) Rs. 24000
Each half (200 m) costs Rs. 12000
Target selling price for a 12% gain \(=24000\times1.12=\) Rs. 26880
The second half (what is left of the target after the first half):
First half sold at 4% profit: \(12000\times1.04=\) Rs. 12480
The second half must fetch \(26880-12480=\) Rs. 14400
Profit on it \(=14400-12000=2400\)
As a per cent of its cost: \(\displaystyle \frac{2400}{12000}\times100=20\%\)
Shortcut: The two halves cost the same, so the gain on the whole is the simple average of the two gains.
\(\displaystyle \frac{4+x}{2}=12\)
\(4+x=24\), so \(x=20\%\)