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

In a two digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that product of the given number and the sum of its digits is equal to 144, then the number is- Correct Answer 24

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 (ans)

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