Question

8. 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.