Question

A two digit number 9 is 4 times the sum of its digits, if 18 is added to the number. The digit interchange their places find the number

Answer 1

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

Answer: The two-digit number is 24.