Averages, simple average, arithmetic mean problems : CAT XAT SNAP MBA Entrance classes, Correspondence courses

Question 4 the day : March 27, 2003
The question for the day is from the topic Averages. The question is a CAT 2002 question.

Question
A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What was the difference of the two digits a and b?

1. 8
2. 6
3. 2
4. 4

Correct Answer - 2. Choice (3) is right.

Explanatory Answer

Let the original number be ab i.e., (10a + b).
After interchanging the digits, the new number becomes ba i.e., (10b + a).

The question states that the average of 10 numbers has become 1.8 less than the original average. Therefore, the sum of the original 10 numbers will be 10*1.8 more than the sum of the 10 numbers with the digits interchanged.

i.e., 10a + b = 10b + a + 18, 9a - 9b = 18, a - b = 2.

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