A student finds the average of nine positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say pq for qp. Due to this, the average becomes 1 less than the previous one. What was the difference of the two digits p and q?
Let the original number be pq i.e., (10p + q).
After interchanging the digits, the new number becomes qp i.e., (10q + p).
The question states that the average of 9 numbers has become 1 less than the original average.
Therefore, the sum of the original 9 numbers will be 9*1 more than the sum of the 9 numbers with the digits interchanged.
i.e., 10p + q = 10q + p + 9
=> 9a - 9b = 9
=> a - b = 1.
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