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

Solution(By Examveda Team)

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
⇒ 22x² + 26x - 140 = 0
⇒ 11x² + 13x - 70 = 0
⇒ 11x² + (35 - 22)x - 70 = 0
⇒ 11x² + 35x - 22x - 70 = 0
⇒ (x - 2)(11x + 35) = 0
⇒ x = 2
Hence, required number = 11x + 2 = 24