In a two-digit, its unit digit exceeds its ten-digit by 2, and that the product of the given number and the sum of its digit is equal to 460. The number is :
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 46
Let the ten's digit number be 10x + y.
y = x + 2
According to the question,
(10x + y)(x + y) = 460
(10x + x + 2)(x + x + 2) = 460
(11x + 2)(2x + 2) = 460
(11x + 2)(x + 1) = 230
At x = 4 given condition satisfies,
(44 + 2)(4 + 1) = 230
46 × 5 = 230
230 = 230
y = 4 + 2 = 6.
Required number = 10 × 4 + 6 = 46.