A two – digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.
Let the digits at units and tens places be x and y respectively.
Original number = 10y + x
According to the question
10y + x = 4(x + y)
10y + x = 4x + 4y
3x – 6y = 0
x = 2y – – – – (1)
also,
10y + x = 2xy
Using (1)
10y + 2y = 2.2y.y
12y = 4y2
y = 3
From (1) we get
x = 2.3 = 6
Original number = 10y + x
= (10.3) + 6 = 36