In a two-digit, if it is known that its unit’s digit exceeds its ten’s digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:

Question:
In a two-digit, if it is known that its unit’s digit exceeds its ten’s digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:

[A].

24

[B].

26

[C].

42

[D].

46

Answer: Option A

Explanation:

Let the ten’s digit be x.

Then, unit’s digit = x + 2.

Number = 10x + (x + 2) = 11x + 2.

Sum of digits = x + (x + 2) = 2x + 2.

(11x + 2)(2x + 2) = 144

22×2 + 26x – 140 = 0

11×2 + 13x – 70 = 0

(x – 2)(11x + 35) = 0

x = 2.

Hence, required number = 11x + 2 = 24.