Question : Sujatha sold 75% of her goods at a profit of 24% and the remaining at a loss of 40%. What is her gain or loss percentage on the whole transaction?
Option 1: 8% gain
Option 2: 10% gain
Option 3: 7.5% loss
Option 4: 9% loss
Correct Answer: 8% gain
Solution :
Let the total goods be 100 and their value is 100.
So, total cost price = 100 × 100 = 10000
Sujatha sold 75% of her goods at a profit of 24%.
So, the selling price = 75 × (100 + 24) = 75 × 124 = 9300
She sold the remaining at a loss of 40%.
So, the selling price of the remaining = (100 – 75) × (100 – 40) = 25 × 60 = 1500
Total selling price = 9300 + 1500 = 10800
Gain = 10800 – 10000 = 800
Profit percentage = $\frac{\text{profit}}{\text{Cost price}}×100=\frac{800}{10000}×100=8\%$
Hence, the correct answer is a gain of 8%.
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