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 = 4y^{2}

y = 3

From (1) we get

x = 2.3 = 6

Original number = 10y + x

= (10.3) + 6 = 36

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