A Two number is 4 times the sum of its digits. The sum of the number formed by reversing its digits and 9 is equal to 2 times the original number. Find the number.

Answer 1

I assume you meant: A two digit number ...

Let the tens digit be x, let the unit digit be y
Then the originial number is 10x + y
and the number reversed is 10y + x

10x + y = 4(x+y)
10x + y = 4x + 4y
6x - 3y = 0
2x - y = 0 OR y = 2x

"The sum of the number formed by reversing its digits and 9 is equal to 2 times the original number"
---> 10y+x + 9 = 2(10x + y)
10y + x + 9 = 20x + 2y
8y = 19x - 9
8(2x) = 19x - 9
use substitution:
16x - 19x = -9
x = 3 , then y = 6

Then the original number was 36

check: is the sum of its digit equal to 9 ? YES
The number reversed is 63
is 63 + 9 = 2(36) ? , YES

All is good