Question

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.
1. 4
2. 5
3. 2
4. 6

Answer 1

Correct Answer - Option 1 : 4

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

∴ difference between two digits is 4