Let the digit in the ones place be x and tens place be y
Hence the two digit number = 10y + x
Given that the two digit number = 4 times sum of its digits
⇒ 10y + x = 4(x + y)
⇒ 10y + x = 4x + 4y
⇒ 3x – 6y = 0
⇒ 3x = 6y
∴ x = 2y → (1)
It is also given that the two digit number = 2 times product of its digits
⇒ 10y + x = 2xy
Divide by xy both the sides, we get
10/x + 1/y =2
put x =2y from 1, we get
6/y = 3
so y = 2 and hence x= 6
Hence x = 6
The two digit number is (10y + x) = 10(3) + 6 = 36
