Question

a two digit number is 4 times the sum and three times the product of its digits find the number

Answer 1

let the number is 10x + y

now

10x+y = 4(x+y) and 10x+y = 3xy

10x+y = 4x+4y

6x = 3y

y = 2x

Since y = 2x and 10x+y = 3xy, we have 10x+2x=3x(2x)

12x = 6x2 6x2-12x = 0

6x(x-2) = 0 x = 0 or x = 2

Since x can't be zero, x = 2

y = 2x = 4

The number is 24.

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the unit digit and tens digit of the two digit number be x and y respectively.

Number = 10y + x

According to the Question,

⇒ 10y + x = 4(y + x)

⇒ 10y + x = 4y + 4x

⇒ 10y - 4y = 4x - x

⇒ 6y = 3x

⇒ 2y = x  ... (i)

Also, 10y + x = 3xy .... (ii)

⇒ 10y + 2y = 3(2y)y   [From Eq (i)]

⇒ 12y = 6y²

⇒ 6y² - 12y = 0

⇒ 6y(y - 2) = 0

⇒ y = 0, 2

Rejecting y = 0 as tens digit should not be zero for two digit number

⇒ x = 4

Number = 10y + x = 10 × 2 + 4 = 24.

Hence, the required number is 24.