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The average of twelve 2 digit numbers is decreased by 3 when the digits of one of the 2 digit numbers is interchanged. Find the difference between the digits of that number.
  • a)
    4
  • b)
    5
  • c)
    2
  • d)
    6
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The average of twelve 2 digit numbers is decreased by 3 when the digit...
Given:
The average of twelve 2 digit numbers is decreased by 3 when the digits of one of the 2 digit numbers is interchanged.
Formula used:
Average = sum of observations/ Number of observations
Calculation:
Let the number whose digits are being interchanged is 10x + y
After interchanging the digits, the number becomes 10y + x
At first average = (sum of 11 numbers + 10x + y)/12
After interchanging the digits,
average = (sum of 11 numbers + 10y + x)/12
So,
(sum of 11 numbers + 10y + x)/12 = (sum of 11 numbers + 10x + y)/12 - 3
⇒ (sum of 11 numbers + 10y + x) = (sum of 11 numbers + 10x + y) - 36
⇒ 10y + x = 10x + y - 36
⇒ 9x - 9y = 36
⇒ x - y = 36/9 
⇒ x - y = 4
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The average of twelve 2 digit numbers is decreased by 3 when the digits of one of the 2 digit numbers is interchanged. Find the difference between the digits of that number.a)4b)5c)2d)6Correct answer is option 'A'. Can you explain this answer?
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