A boy was asked to calculate the arithmetic mean of ten positive integers each of which had 2 digits.
By mistake, he interchanged the two digits, a & b, in one of these ten integers. As a result, his answer for the arithmetic mean was 1.8 more than what it should have been.
Find the value of b-a.

If the mean was 1.8 higher, the sum of the numbers was 18 higher, which means the interchanged numbers had a difference of 18/9 = 2. (This is an old trick used by accounting people to find mistyped numbers.)

Posted by Federico Kereki on 2003-11-19 11:58:44