Question

in a two digit number the tens digit is 6 more than the units digit. if the digits are interchanged, the sum of the new and the original number is 132. Determine the original number.​

Answer 1

Given:

In a two digit number the tens digit is 6 more than the units digit.

If the digits are interchanged, the sum of the new and the original number is 132.

To find:

The original number.

Solution:

Let the unit digit of the original number be x. So, the tens digit is (x+6) and the value of the number is:

`m=(x+6)* 10+x* 1`

`m=10x+60+x`

`m=11x+60`

If we interchange the digits, then the value of new number is:

`n=x* 10+(x+6)* 1`

`n=10x+x+6`

`n=11x+6`

The sum of the new and the original number is 132.

`m+n=132`

`11x+60+11x+6=132`

`22x+66=132`

`22x=132-66`

`22x=66`

Divide both sides by 22.

`x=(66)/(22)`

`x=3`

So, the unit digit of the original number is 3 and the tens digit is:

`x+6=3+6`

`x+6=9`

Therefore, the original number is 39.