Question

A two-digit number is 4 times the sum of its digits. If 18 is added to the number, the digits
are reversed. Find the number.
[CBSE 2001C)

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.