Question

A two digit number is four times the sum of its digits . it is also equal to three times the product of its digits . find the numbers

Answer 1

Let the unit digit be x
and tens digit be y

The two digit number is :- 10y + x

• Number is 4 times the sum of digit

10y + x = 4 ( x + y )

10y + x = 4x + 4y

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

6y - 3x = 0

( dividing by 3 )

2y - x = 0

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

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

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


Putting the value of y in equation ii

10y + x = 3xy

10 × ( x/2 ) + x = 3 x ( x/2 )

5x + x = 3x² /2

6x = 3x²/2

12x = 3x²

12x/3x = x

6 = x

Putting the value of x in equation i

y = x/2

y = 3


The required number is

10y + x

10 × 3 + 6

30 + 6

36

Answer 2

Answer:

Refers to the attachment