Question

A two digit number is 4 times the sum of the digit. It is also equal to 3 time the products of digots .Find the numbers

Answer 1

Let the tens place be 'y' and units place be 'x'

By Qn,

10y+x=4x+4y
ie
6y=3x
ie
2y=x-----(1)

Again By Qn,
10y+x=xy
ie
$10y + 2y = {2y}^{2}$
ie
$5y + y = {y}^{2}$
ie
$y = 6$
ie
(1)》 x=2y=2(6)=12

Thus the no. is 72

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