Let’s assume the digit at unit’s place is x and at ten’s place is y. 

Thus from the question, the number we need to find is 10y + x. 

From the question since the number is 4 times the sum of the two digits. We can write, 

10y + x = 4(x + y)

⇒ 10y + x = 4x + 4y 

⇒ 4x + 4y – 10y - x = 0

⇒ 3x – 6y = 0

⇒ 3(x – 2y) = 0

⇒ x – 2y = 0 ……………… (i) 

Secondly, after reversing the digits, the new number formed is 10x + y. 

Again it’s given from the question that if 18 is added to the original number, the digits are reversed. Thus, we have 

(10y + x) + 18 = 10x + y 

⇒ 10x + y - 10y – x = 18

⇒ 9x – 9y = 18

⇒ 9(x -y) = 18

⇒ x – y = 18/9

⇒ x - y = 2 …………. (ii) 

Now by solving equation (i) and (ii) we can find the value of x and y and thus the number.

On subtracting the equation (i) from equation (ii), we get; 

(x - y) – (x – 2y) = 2 - 0 

⇒ x – y – x + 2y = 2

⇒ y = 2 

Putting the value of y in the equation (i) to find x, we get 

x – 2 x 2 = 0 

⇒ x – 4 = 0 

⇒ x = 4 

Hence, the required number is 10 x 2 + 4 = 24