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.

(X + Y)/10 - (X + Z)/10 = 1.8

X = sum of the 9 positive integers with 2 digits
Y = ba
Z = ab

Y - Z = 18
Therefore,
(y,z) = (31,13) ; (42,24); . . .;(97,79)
In each case (b - a) = (-2).

Posted by wonshot on 2003-11-19 12:30:30