A two-digit number is 4 times the sum of its digits and twice the product of the digits. The number is:

Correct option is C

Let the two-digit number be 10x + y, where x is the tens digit and y is the units digit.
Then:

Number = 4 × (x + y)

Number = 2 × (x × y)

Formula used:
10x + y = 4(x + y) ...(1)
10x + y = 2xy ...(2)

Solution:
From (1):
10x + y = 4x + 4y
=> 6x - 3y = 0
=> 2x = y ...(A)

Substitute (A) in (2):
10x + y = 2xy
=> 10x + 2x = 2x × 2x
=> 12x = 4x²
=> 4x² - 12x = 0
=> 4x(x - 3) = 0
=> x = 0 or x = 3

Reject x = 0 (since the number wouldn't be two-digit)
So, x = 3 => y = 2x = 6
Number = 10x + y = 30 + 6 = 36

Correct answer is (c)