If Sohan, 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.
- 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%.
▶ Answer & Explanation
Correct answer: C. he suffers a loss of 1%.
When an item is sold at the same selling price, with one sold at a profit and the other at a loss by the same percentage, there is always an overall loss. Let the selling price of each goat be Rs. 100. For the first goat sold at a 10% profit, the cost price would be Rs. 100 / 1.10 = Rs. 90.91. For the second goat sold at a 10% loss, the cost price would be Rs. 100 / 0.90 = Rs. 111.11. The total cost price is Rs. 90.91 + Rs. 111.11 = Rs. 202.02. The total selling price is Rs. 100 + Rs. 100 = Rs. 200. Therefore, there is a loss of Rs. 2.02 on a total cost of Rs. 202.02, which is approximately 1% loss. In general, if two items are sold at the same selling price, one at x% profit and the other at x% loss, the net result is always a loss of (x/10)^2 %.
Source: UPSC csat 2014