Question

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

Answer 1

Hello.

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.

Hope it helps.

Answer 2

let unit digit be x
ten's digit be y
no is 10y+x
ATQ
10y+x=4(x+y)
10y+x=3xy