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Q.
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 :
A.
12
B.
24
C.
36
D.
48
View Answer
Correct choice: B
Explanation:
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 => 22x^2+26x-140=0 => (x - 2)(11x + 35) = 0 => x = 2 Hence, Required Number = 11x + 2 = 24
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