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%
Let’s solve it step by step.
Step 1: Cost Price (CP)
- Total wire = 500 m
- CP per m = 50 paise = ₹0.50
$\text{Total CP} = 500 \times 0.50 = ₹250$
Step 2: Selling 50% wire
- 50% of 500 m = 250 m
- CP of 250 m = $250 \times 0.50 = ₹125$
Profit = 5%
$\text{SP}_1 = 125 \times 1.05 = ₹131.25$
Step 3: Required total SP for 10% overall gain
$\text{Total SP} = 250 \times 1.10 = ₹275$
So, SP required from remaining 250 m:
$275 - 131.25 = ₹143.75$
Step 4: Find profit % on remaining wire
- CP of remaining 250 m = ₹125
Profit on remaining wire:
$143.75 - 125 = ₹18.75$
$\text{Profit}\% = \frac{18.75}{125} \times 100 = 15\%$
Correct answer: 15%