Question

a two digit number is 4 times the sum of the digits it is also equal to 3 times the product of the digits find the number

Answer 1

Let the 2 digits be x and y
10x+y=4(x+y)--------------1)
y=4x+4y-10x
y =4y-6x
-3y=-6x
3y=6x
 y=2x 
10x+y=3xy------------------2)
4x+4y=3xy
4x+8x=6$x^{2}$
12x=6$x^{2}$
6x=12
x=2

y=2x
∴y=4
THE NUMBER IS 24
CHEERS!!

Answer 2

Hi there...
here is the solution

let the two digits are X and Y
then the number is (10x+y)

now, according to question

(10x +y) =4(x +y)
=> 6x =3y
=> x = y/2 ........eq.(1)

also,
(10x+y) =3xy.......eq.(2)

put x=y/2 in eq.(2)

then,
10(y/2) + y = 3(y/2)y
=>5y +y = 3y²/2
=>3y²/2 -6y =0
multiplying by 2
=> 3y² -12y = 0
=>3y(y-4) =0
now either 3y =0 or, y-4=0
that is y = 0 , 4
then, x= y/2 = 0/2 =0
or, x = 4/2 = 2
here we consider nonzero values because the number is two digits
then, x=2 and y=4
Hence the number is (10×2 +4) =24
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Hope it helps......