Question : A man bought 500 metres of electronic wire at 50 paise per metre. He sold 50% of it at a profit of 5%. At what percentage should he sell the remainder so as to gain 10% on the whole transaction?
Option 1: 13%
Option 2:
12.5%
Option 3:
15%
Option 4:
20%
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Correct Answer:
15%
Solution :
The cost price of the electronic wire = Rs. 0.50 per metre.
The man bought 500 metres, so the total cost price = Rs. 0.50 × 500 = Rs. 250
He sold 50% of it at a profit of 5%.
The selling price of these 250 metres = Rs. 0.50 × 250 × 1.05 = Rs. 131.25
The man wants to gain 10% on the whole transaction.
The total selling price for all 500 metres = Rs. 250 × 1.10 = Rs. 275
The selling price of the remaining 250 metres = Rs. 275 – Rs. 131.25 = Rs. 143.75
The selling price of each of the remaining metres = $\frac{143.75}{ 250}$ = Rs. 0.575
Percentage gain = $\frac{\text{Selling price – Cost price}}{\text{Cost price}}$ × 100%
The percentage gain on each of these metres = $\frac{0.575 - 0.50}{ 0.50}$ × 100 = 15%
Hence, the correct answer is 15%.
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