Q.4. A 2 digit number is 4 times the sum of its digits. If 18 is added to the number, the new number obtained is that by interchanging the digits of the original number. Find the number.

Let the digits be x and y

Then the two-digit number is 10x + y

Given that: 10x + y = 4 (x + y) 

       10x + y = 4x + 4y

        6x = 3y

          y = 2x  ---------------( 1)

And 10x + y + 18 = 10y + x

Or           9y – 9x = 18 ---------------- (2)

Substitute the value of y in eqn( 2)

18x – 9x = 18

9x = 18

x = 2

Therefore  y = 2x = 2*2 = 4

And the number is 10x + y = 10*2 + 4 = 24