Question

A two digit number is 4 Tims the sum of the digits it is also equal to three times the product of digits find them ????

Answer 1

let say number = xy

then value of number = 10x +y

sum of digit = x +y

product of digits = xy

10x+y = 4(x+y)

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

=> 6x = 3y

=> 2x = y

10x +y = 3xy

putting value of y = 2x in equation

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

=> 12x = 6x(x)

=> 2 = x

x = 2

y = 2x = 4

number = 24

Answer 2

Let the digit at ones place be 'y' and the digit at tenth place be 'x'.

So,the two digit no. is 10x+y.

Sum of the digits = x+y

Product of the digits = x × y = xy.

Now, A/Q

=> 10x + y = 4(x+y) ––––> [1]

=> 10x + y = 3(xy). ––––> [2]

Now, by solving [1], we get

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

=> 10x - 4x = 4y - y

=> 6x = 3y

=> y = 2x ––––>[3]

By solving [2],we get

=> 10x + y = 3xy

=> 10x + 2x = 3x(2x) [putting y = 2x]

=> 12x = 6x^2

=> 12 = 6x

=> x = 2

Now, putting x=2 on equation [3],we get

=> y = 2x

=> y = 2(2)

=> y = 4.

Therefore our required no. is

=10x+y

=10(2)+4

=20+4

=24

$\boxed{answer = 24}$