The product of the digits of a two digit number is 24. If it's unit's digits exceeds twice it's ten's digit by 2; find the number.

Let unit's digit be x and ten's digit be y.

According to question,

⇒ xy = 24 ……..(i)

⇒ x = 2y + 2 ……..(ii)

Substituting value of x from (ii) in (i) we get,

⇒ (2y + 2)y = 24

⇒ 2y² + 2y = 24

⇒ y² + y = 12

⇒ y² + y - 12 = 0

⇒ y² + 4y - 3y - 12 = 0

⇒ y(y + 4) - 3(y + 4) = 0

⇒ (y - 3)(y + 4) = 0

⇒ y - 3 = 0 or y + 4 = 0

⇒ y = 3 or y = -4.

Since digit at ten's place cannot be negative

∴ y ≠ -4.

⇒ x = 2y + 2 = 2(3) + 2 = 8

Number = 10(y) + x = 10(3) + 8 = 38.

Hence, number = 38.