Question 4 the day : April 4, 2002
The question for the day is a sample practice problem in profit, loss, discounts, an Arithmetic Topic and the problem provides an understanding of the different terms such as Cost Price, List Price, Selling price and margins.

Question
A merchant buys two articles for Rs.600. He sells one of them at a profit of 22% and the other at a loss of 8% and makes no profit or loss in the end. What is the selling price of the article that he sold at a loss?

1. Rs.404.80
2. Rs.440
3. Rs.536.80
4. Rs.160

Correct Answer - Rs.404.80 . Choice (1)

Explanatory Answer

Let C1 be the cost price of the first article and C2 be the cost price of the second article.
Let the first article be sold at a profit of 22%, while the second one be sold at a loss of 8%.

We know, C1 + C2 = 600.
The first article was sold at a profit of 22%. Therefore, the selling price of the first article = C1 + (22/100)C1 = 1.22C1
The second article was sold at a loss of 8%. Therefore, the selling price of the second article = C2 - (8/100)C2 = 0.92C2.

The total selling price of the first and second article = 1.22C1 + 0.92C2.

As the merchant did not make any profit or loss in the entire transaction, his combined selling price of article 1 and 2 is the same as the cost price of article 1 and 2.

Therefore, 1.22C1 + 0.92C2 = C1+C2 = 600
As C1 + C2 = 600, C2 = 600 - C1. Substituting this in 1.22C1 + 0.92C2 = 600, we get
1.22C1 + 0.92(600 - C1) = 600
or 1.22C1 - 0.92C1 = 600 - 0.92*600
or 0.3C1 = 0.08*600 = 48
or C1 = 48/(0.3) = 160.
If C1 = 160, then C2 = 600 - 160 = 440.
The item that is sold at loss is article 2. The selling price of article 2 = 0.92*C2 = 0.92*440 = 404.80.

Note: When you actually solve this problem in CAT, you should be using the following steps only
1.22C1 + 0.92C2 = C1+C2 = 600
1.22C1 + 0.92(600 - C1) = 600
C1 = 48/(0.3) = 160.
C2 = 600 - 160 = 440.
And the final step of the answer which is 0.92*440 which you should not actually compute. As two of the answer choices (2) and (3) are either 440 or more, they cannot be the answers. The last one is way too low to be 92% of 440, therefore, the answer should be choice (1)

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