GATE CS 2024 Set 2 Q.7: Quantitative Aptitude

A person sold two different items at the same price. He made 10% profit in one item, and 10% loss in the other item. In selling these two items, the person made a total of

1% profit

2% profit

1% loss

2% loss

Official answer and solution

Official answer: C
From: Official GATE 2024 answer key

Solution

Express the cost prices of both items in terms of the common selling price $S$ and compare total selling price with total cost price.

Let the selling price of each item be $S = 99$ .

For the first item (10% profit): $C_1 = \frac{99}{1.1} = 90$ .
For the second item (10% loss): $C_2 = \frac{99}{0.9} = 110$ .
Total cost price $= C_1 + C_2 = 90 + 110 = 200$ .
Total selling price $= 2S = 99 + 99 = 198$ .

Since $198 < 200$ , there is a net loss of $\frac{200 - 198}{200} \times 100\% = 1\%$ loss. (In general, selling two items at the same price with $p\%$ gain on one and $p\%$ loss on the other always results in a $\frac{p^2}{100}\%$ loss.)

Final answer

Option (C)

Common trap

Adding $+10\%$ and $-10\%$ directly without noting that the percentages are taken on different cost prices.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2024 Computer Science and Information Technology - Set 2 (CS2)
Question: 7 of 65
Section: General Aptitude

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