Avinash was asked to calculate the arithmetic mean of ten positive integers, each of which had two digits. By mistake, he interchanged the two digits, say a and b, in one of these ten integers i.e. ab. As a result, his answer for the arithmetic mean was 2.7 more than what it should have been. Then, b - a is equal to
Explanation:
Since the average differs by 2.7, the difference in sum will be 2.7 × 10 = 27.
Let the original number is ab.
Let the sum of the rest nine terms be x.
Sum of all 10 numbers including ‘ab’ = x + 10a + b
Sum of all 10 numbers including reverse number ‘ba’ = x + 10b + a
Difference in sum = (x + 10b + a) - (x + 10a + b) = 27
⇒ 9(b - a) = 27
⇒ (b - a) = 3
Alternately, The difference in total due to reversing the number = (10b + a) - (10a + b) = 9(b - a)
Since average increases by 2.7, the total increases by 2.7 × 10 = 27.
Hence, option (d).
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