Question

A two digit number is four times the sum of the digits. It is

also equalto 3 timesthe product of digits. Find the number​

Answer 1

A two digit positive integer can be expressed as 10x+y, where x is the tens digit and y is the ones digit.  For example, 37 = 3(10)+7.

So, 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

good morning mate.

let the ones digit be x

then ten's digit=y

now. case 1

10y+x=4(x+y)

6y-3x=0

now case 2..

10y+x=3xy...

now.

6y-3x=0

6y=3x

x=2y.

substituting the value of x in

10y+x=3xy

10y+2y=6y^2

12y=6y^2

y=2. ( dividing both sides by 6y)

now. x=2y

x=4.

the number is 24.

hope it is correct..