Question

a two digit number is such that it is 4 times the sum of the digit is also equal to 3 times the product. 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

Here is your solutions
 

Let the one's digit be x.

ten's digit be y.

Original number = 10x + y

given that the number is four times the sum of the number, i.e., 4(x + y).

=> 10x + y = 4(x + y)

=> 10x + y = 4x + 4y

=> 10x - 4x + y - 4y = 0

=> 6x - 3y = 0

=> 3(2x - y ) = 0

=> 2x - y = 0

=> 2x = y

given that it is also equal to 3 times the product of digits, i.e, 10x + y = 3xy.

y = 2x and 10x+y = 3xy

on putting value of y = 2x in

=> 10x + y = 3xy.

=> 10x + 2x = 3x( 2x )

=> 12x = 6x²

=> 12x - 6x² = 0

=> 6x ( 2 - x) = 0

So, x = 0 and x = 2

x = 2

On putting value of x in y = 2x.

we get;

y = 2x

=> y = 2 × 2 

=> y = 4

So,

Original number = 10x + y

=> 10 × 2 + 4

=> 20 + 4

=> 24

hope you happy