Question : A cloth merchant sold half of his cloth at a 40% profit, half of the remaining at a 40% loss, and the rest was sold at the cost price. In the total transaction, his gain or loss will be:
Option 1: 20% gain
Option 2:
25% loss
Option 3:
10% gain
Option 4:
15% loss
Correct Answer:
10% gain
Solution :
Let the cost price of the cloth be $\mathrm{Rs.}\;\mathrm{C}$.
The merchant sold half of his cloth at a $40\%$ profit.
The selling price for this part $=\mathrm{0.5C + 0.4 \times 0.5C = 0.7C}$
He sold half of the remaining at a $40\%$ loss.
The selling price for this part $=\mathrm{0.25C - 0.4 \times 0.25C = 0.15C}$
The rest of the cloth was sold at the cost price.
The selling price for this part $=\mathrm{0.25C}$
The total selling price $=\mathrm{0.7C + 0.15C + 0.25C = 1.1C}$
The profit percentage $=\mathrm{\frac{1.1C-C}{C}×100=10\%}$
So, the answer is $10\%$ gain.
Hence, the correct answer is 10% gain.
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