Question

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

Answer 1

Let the tens and the units digits of the required number be x and y.

Number = (10x + y) .

According to the Question,

⇒ 10x + y = 4(x + y) + 3 .

⇒ 10x + y = 4x + 4y + 3 .

⇒ 6x - 3y = 3 .

⇒ 2x - y = 1 ….(i) .

Also, 10x + y + 18 = 10y + x.

⇒ 9x - 9y = -18 .

⇒ x - y = -2 ….(ii) .

Subtracting (ii) from (i), we get

⇒ x = 3 .

Putting x's value in (i), we get

⇒ 2x - y = 1.

⇒ 2 × 3 - y = 1 .

⇒ y = 6 - 1.

⇒ y = 5 .

Number = (10x + y) = 10 × 3 + 5 = 30 + 5 = 35.

Hence, the required number is 35.