Question

a two digit number is 4 times the sum of digits it is also equal to 3 times the product of digits find the number

Answer 1

Let's call the two digit number "ab" 

According to the problem, "ab" = 4(a+b) = 3(a*b) 

"a" and "b" are integers, so "ab" = (10a + b), the same way that "23" = (10*2 + 3). 

_____ 

(10a +b) = 4(a + b) = 3(a * b) 

10a + b = 4a + 4b = 3ab


Let's solve one half of this equation for a, in terms of b: 

10a + b = 4a + 4b ... combine like terms 

6a = 3b ... divide both sides by 3 

2a = b 
_____ 

Now we can substitute the equality (2a = b) in for b: 

10a + b = 3ab ... solve one side at a time: 

5b + b = 3ab 

6b = 3ab ... now divide by 3 

2b = ab ... so a*b = 2*b, therefore a = 2 


Now subsitute the value a = 2 into the equality (2a = b) 

2a = b 

2*2 = b 

b = 4 
_____ 

So the original number is (10a + b) = (10*2 + 4) = (20 + 4) = 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