A shopkeeper buys 500 m of electronic wire at 50 paise per m. He sold 50 % of the wire at a profit of 5%. At what percent should the shopkeeper sell the remaining wire so as to gain 10% on the whole transaction?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 15%
The gain wanted on the whole wire fixes the total selling price; the part already sold is taken away, and what is left must come from the remaining half.
Cost of 500 m at 50 paise per metre \(=500\times0.50=\) Rs 250, so each half costs Rs 125
Selling price for a 10% gain on the whole \(=250\times\frac{110}{100}=\) Rs 275
First half sold at 5% profit: \(125\times\frac{105}{100}=\) Rs 131.25
Remaining half must fetch \(275-131.25=\) Rs 143.75
Profit on it \(=143.75-125=\) Rs 18.75, and \(\displaystyle \frac{18.75}{125}\times100=15\%\)
Shortcut: The two halves cost the same, so the gain on the whole is the simple average of the two rates.
\(\displaystyle \frac{5+x}{2}=10\), so \(x=15\%\)