Question:
Amol was asked to calculate the arithmetic mean of 10 positive integers, each of which had 2 digits. By mistake, he interchanged two digits, say \( a \) and \( b \), in one of these 10 integers. As a result, his answer for the arithmetic mean was 1.8 more than what it should have been. Then \( b - a \) equals:
Amol was asked to calculate the arithmetic mean of 10 positive integers, each of which had 2 digits. By mistake, he interchanged two digits, say \( a \) and \( b \), in one of these 10 integers. As a result, his answer for the arithmetic mean was 1.8 more than what it should have been. Then \( b - a \) equals:
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When working with averages, check how changes in individual numbers affect the overall mean.
Updated On: Mar 24, 2026
- 1
- 2
- 3
- None of these
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The Correct Option is B
Solution and Explanation
Let the original sum of the numbers be \( S \), and the sum after interchanging \( a \) and \( b \) be \( S' \). The difference in the mean is:
\[
\frac{S' - S}{10} = 1.8.
\]
Thus, \( S' - S = 18 \). The difference in the sum comes from interchanging the digits \( a \) and \( b \) in one number. The difference in the value is \( 10b + a - (10a + b) = 9b - 9a = 9(b - a) \). Thus:
\[
9(b - a) = 18 \Rightarrow b - a = 2.
\]
Hence, the Correct Answer is \( b - a = 2 \).
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