Multiple choice

A student 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 greater than 100. By mistake, the student interchanged the 2 digits of the marks (mn) of one student. As a result, the average of marks calculated for the ten students was 2.7 more than what it would have been. What could be the value of n – m?

  1. 1

  2. 2

  3. 3

  4. 4

  5. 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the marks be 10m + n. Interchanged, they become 10n + m. Difference = (10n + m) - (10m + n) = 9(n - m). The average change is 2.7, so the total sum change is 2.7 * 10 = 27. 9(n - m) = 27 => n - m = 3.

AI explanation

Using the average deviation method, the total increase in the sum of the marks is 10 multiplied by 2.7, which equals 27. Interchanging the digits of a number mn to nm gives a difference of (10n + m) minus (10m + n), simplifying to 9(n minus m). Setting this equal to the total increase gives 9(n minus m) equals 27, so n minus m equals 3.

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