Question

The average of nine 2 digit numbers is decreased by 6 when the digits of one of the 2 digit numbers is interchanged. Find the difference between the digits of that number.
1. 6
2. 8
3. 2
4. 4

Answer 1

Correct Answer - Option 1 : 6

Given 

The average of nine 2 digit number decreases by = 6

Formula Used 

Average = sum of observation/ No. of observation

Calculation

Let the number be 10x+y

(sum of eight numbers + 10x + y)/9 - 6 = (sum of eight numbers + 10y + x)/9

⇒(sum of nine numbers + 10x + y) - 54 = (sum of nine numbers + 10y + x)

⇒10x + y + 54 = 10y + x

⇒54 = 9y - 9x 

⇒ y-x = 6

∴ The difference between the digit of number is 6.