perplexus.info :: Just Math : Calculation Mistake

Calculation Mistake (Posted on 2003-11-19)

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.

Submitted by Ravi Raja

Rating: 2.2857 (7 votes)

Solution: (Hide)

Let the sum of the first 9 numbers be X and the 10th number be of the form (10a + b). Then according to the problem, we have the following relation:
[{X + (10b + a)}/10] - [{X + (10a + b)}/10] = 1.8
or, [(10b + a) - (10a + b)]/ 10 = 1.8
or, 9(b - a) = 18
or, b - a = 2

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Solution	K Sengupta	2007-09-30 05:49:06
re: a short one	Justin	2005-05-21 02:02:28
a short one	Mike	2003-11-20 07:23:52
solution	wonshot	2003-11-19 12:30:30
Short	Federico Kereki	2003-11-19 11:58:44
Layman's analysis of a solution	Andy	2003-11-19 11:11:43
solution	ben	2003-11-19 09:46:11
Solution	fwaff	2003-11-19 09:38:00

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