Multiple choice

Ram was given the task to calculate the average marks of ten students of the class. It was known that none of the students scored less than 10 or more than 100 marks. By mistake, Ram interchanged the two digits of the marks of Shyam. As a result, the average of marks calculated for the ten students were 2.7 more than what it would have been. What could be positive difference of the digits of the marks of Shyam?

  1. 1

  2. 2

  3. 3

  4. 4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the marks be 10x + y. Interchanging gives 10y + x. The difference in marks is |(10y+x) - (10x+y)| = |9(y-x)|. The average difference is 2.7, so the total sum difference is 2.7 * 10 = 27. Thus, 9|y-x| = 27, which means |y-x| = 3.

AI explanation

When a two-digit number with tens digit a and units digit b is reversed, the difference between the new number and the original number is 9 times the positive difference of the digits. The total increase in marks for the 10 students is 2.7 times 10, which equals 27. Therefore, 9 times the difference of the digits equals 27, making the difference of the digits 3.

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