Question

A number of 2 digits is equal to the four time the sum of its digits. If 8 is added to the number the digits are reversed. 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

10x - 4x = 4y - y

6x = 3y

y = 6x/3

y = 2x  --------------- 1

And 10x + y + 8 = 10y + x

10x - x + y - 10y = -8

9x - 9y = -8

9y – 9x = 8 ---------------- 2

Substitute the value of y in eqn 2

18x – 9x = 8

9x = 8

x = 8/9

Therefore  y = 2x = 2 x 8/9 = 16/9

And the number is 10x + y = 10 x 8/9 + 16/9

= 80/9 + 16/9

= (80 + 16)/9

= 96/9

= 32/3

Answer: The two-digit number is 32/3.