Question
In a two-digit, 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:
Answer: Option A
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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.
Therefore (11x + 2)(2x + 2) = 144
\(\Rightarrow\) 22x2 + 26x - 140 = 0
\(\Rightarrow\) 11x2 + 13x - 70 = 0
\(\Rightarrow\) (x - 2)(11x + 35) = 0
\(\Rightarrow\)x = 2.
Hence, required number = 11x + 2 = 24.
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