Question

the sum of 2 digit number and the number obtained by reversing the digit is 110 the differnece between the digit is 4 find the number

Answer 1

the number is 73 and 37

Answer 2

Let the 2-digit no. be 10x + y, then
10x + y +10y + x = 110
⇒11x + 11y = 110
⇒x + y = 10
⇒x = 10 - y                      ..............(i)

Now,
10x + y - 10 = 5(x + y) + 4
⇒ 10x + y = 5x + 5y + 14
⇒ 5x - 4y = 14                  .............(ii)

Substituting (i) in (ii), we get
50 - 5y - 4y = 14
⇒ -9y = -36
⇒ y = 4
∴ x = 6
2-digit no. is 6x + y = 60 +4 = 64

__________
HOPE IT HELPS