Question:
In a two-digit, 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].24
26
42
46
In a two-digit, 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].
[B].
[C].
[D].
Answer: Option A
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
22×2 + 26x – 140 = 0
11×2 + 13x – 70 = 0
(x – 2)(11x + 35) = 0
x = 2.
Hence, required number = 11x + 2 = 24.