Question

The sum of a number of 2 digits and of the number formed by reversing the digits is 110,and the difference of the digits is 6. Find the number.

Answer 1

Solution-:
let a = the 10's digit
let b = the unit's digit
$\therefore$ the two-digit number = 10a+b
The difference between the digits of a digit number is 6.
$\therefore$ a - b = 6-----(i)
The sum of the numbers and the number formed by reversing its digit is 110.
$\therefore$ (10a+b) + (10b+a) = 110
$\Rightarrow$ 11a + 11b = 110

On dividing 11a + 11b = 110 by 11, we get

a + b = 10-----(ii)

Solving (i) and (ii) by elimination method, we get
a - b = 6
a + b = 10
2a = 16
$\therefore$ a = 8
Putting the value of a = 8 in (ii), we get
8 + b = 10

$\Rightarrow$ b = 10 - 8
$\therefore$ b = 2
So, the number will be 10a+b=10(8)+2=80+2=82