In a two digit number if it is known that its units digit

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In a two digit number if it is known that its units digit exceeds its tens 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

1. 46
2. 42
3. 26
4. 24

Correct Option: D

Let the ten’s digit be x
∴ Unit’s digit = x + 2
Therefore, the two digit number
= 10x + x + 2
= 11x + 2 ...(i)
Again,
(11x + 2) (x + x + 2)
= 144
⇒ (11x + 2) (2x + 2) = 144
(11x + 2) (x + 1) = 72
⇒ 11x² + 2x + 11x + 2 = 72
⇒ 11x² + 13x – 70 = 0
⇒ 11x² – 22x + 35x – 70 = 0
⇒ 11x (x – 2) + 35 (x – 2) = 0
⇒ (x – 2) (11x + 35) = 0

⇒ x= 2 , −	35
	11

⇒ x= 2 , −	35
	11

is not admissible.
∴ The number = 11x + 2
= 11 × 2 + 2 = 24