1.

In a two-digit number, 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:

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 

2x2 + 26x - 140 = 0 

(x - 2)(11x + 35) = 0 

x = 2

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



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