Let unit’s digit = y
and the ten’s digit = x
So, the original number = 10x + y
The sum of the number = 10x + y
The sum of the digit = x + y
According to the question,
10x + y = 3 + 4(x + y)
⇒ 10x + y = 3 + 4x + 4y
⇒ 10x + y – 4x – 4y = 3
⇒ 6x – 3y = 3
⇒ 2x – y = 1 …(i)
The reverse number = x + 10y
and 10x + y + 18 = x + 10y
⇒ 10x + y + 18 = x + 10y
⇒ 10x – x + y – 10y = – 18
⇒ 9x – 9y = – 18
⇒ x – y = – 2 …(ii)
On subtracting Eq. (i) from Eq. (ii) , we get
x – y – 2x + y = – 2 – 1
⇒ – x = – 3
⇒ x = 3
On substituting the value of x = 3 in Eq. (i), we get
2(3) – y = 1
⇒ 6 – y = 1
⇒ – y = 1 – 6
⇒ – y = – 5
⇒ y = 5
So, the Original number = 10x + y
= 10×3 + 5
= 30 + 5
= 35
Hence, the two digit number is 35.