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

Answer 1

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.

Answer 2

Let x be units digit and y be the 10s digit

10y+x = 4(x+y)

10y + x = 4x +4y

6y-3x = 0

2y - x = 0 ————-(1)

When 18 is added to the number

10y + x +18 = 10x + y

Simplify

9y - 9x = -18

y - x = - 2

y = x - 2 —————-(2)

Substitute in equation #1

2(x-2) - x = 0

2x - 4 - x=0

x = 4

Substitute in equation#2

y = 2

There for the number is

2 x 10 + 4 = 24