A two - digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.

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.