UP Police Constable Exam Model Paper 5

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 $10\mathit{x}+\mathit{y}$
After interchanging the digits, the number becomes $10\mathit{y}+\mathit{x}$
At first average $=($ sum of 11 numbers $+10\mathit{x}+\mathit{y})/12$
After interchanging the digits,average $=($ sum of 11 numbers $+10\mathit{y}+\mathit{x})/12$
So,
(sum of 11 numbers $+10\mathit{y}+\mathit{x})/12=($ sum of 11 numbers $+10\mathit{x}+\mathit{y})/12-3$
$\mathrm{Rightarrow}$ (sum of 11 numbers $+10\mathit{y}+\mathit{x})=($ sum of 11 numbers $+10\mathit{x}+\mathit{y})-36$
$\Rightarrow 10\mathit{y}+\mathit{x}=10\mathit{x}+\mathit{y}-36$
$\Rightarrow 9\mathit{x}-9\mathit{y}=36$
$\Rightarrow \mathit{x}-\mathit{y}=36/9$
$\Rightarrow \mathit{x}-\mathit{y}=4$
$\therefore$ difference between two digits is 4