Question

A two digit no. is 4 times the sum of its digits. it is also equal to3 times the product of its digits.find the no.

Answer 1

Let the unit digit be x

and tens digit be y


Two digit number:- 10y + x

• Number is 4 times of the sum of it's digit.

10y + x = 4 ( x + y )

10y + x = 4x + 4y

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

6y - 3x = 0

( dividing by 3 )

2y - x = 0

-x = -2y

x = 2y ....... ( i )


• Number is equal to 3 times the product of it's digit

10y + x = 3xy .....( ii )

Putting the value of x from equation ( i ) in equation ( ii )

10y + x = 3xy

10y + 2y = 3 × 2y ×y

12y = 6y²

12y/6y = y

3 = y


Putting the value of y in equation ( i )

x = 2y

x = 6


The required two digit number is

10y + x

10 × 3 + 6

= 30 + 6

= 36