If Soham while selling two goats at the same price, makes a profit of 10% on one goat and suffers a loss of 10% on the other one (UPSC 2014)a. He makes no profit and no loss.b. He makes a profit of 1%c. He suffers a loss of 1%d. He suffers a loss of 2%
Question
If Soham while selling two goats at the same price, makes a profit of 10% on one goat and suffers a loss of 10% on the other one (UPSC 2014)a. He makes no profit and no loss.b. He makes a profit of 1%c. He suffers a loss of 1%d. He suffers a loss of 2%
Solution
The correct answer is d. He suffers a loss of 2%.
Here's the step-by-step explanation:
Let's assume the cost price of each goat is $100 (for simplicity).
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When Soham sells the first goat at a 10% profit, the selling price becomes 100 is 100 + 110).
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When he sells the second goat at a 10% loss, the selling price becomes 100 is 100 - 90).
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So, the total cost price for the two goats is 100 + 200 (90).
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Although it seems like he neither makes a profit nor a loss because the total cost price and total selling price are the same, this is not the case. The correct way to calculate the overall profit or loss percentage is to take the average of the profit and loss percentages, which in this case is (10% - 10%)/2 = 0%.
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However, this is a common misconception. The correct way to calculate overall profit or loss when the percentages are equal and opposite is to square the common percentage and divide by 100. So, (10^2)/100 = 1% loss. But since this happens twice (once for each goat), the total loss is 2%.
So, he suffers a loss of 2%.
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