# A two-digit number is four times the sum of its digits and twice the product of the digits. Find the number.

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by dweejareddy

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by dweejareddy

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Given: Two-digit number = 4 times sum of its digits

10x + y = 4(x + y)

⇒ 10x + y = 4x + 4y

⇒ 6x = 3y

x = y/2.... (1)

Given: Two-digit number = Twice the product of its digits

⇒ 10x + y = 2(xy)

⇒10x + y – 2xy = 0 …(2)

substituting x= y/2 from equation (1) and equation (2) we get

10 * y/ 2 + y - 2 * y / 2* y = 0

⇒5y + y – y2 = 0

⇒y2 – 6y = 0

⇒y (y – 6) = 0

⇒ y = 0 or y – 6 = 0

We reject y = 0 because then x would also be zero.

Therefore, y = 6

Substituting this value of y in equation 1, we get

x = 6/ 2 = 3

Hence required number is

(10 × 3 + 6) = 36