Question

The sum of the numerator and denominator of a fraction is4 more than the twice the numerator.if 3is added to each of numerator and denominator the ratio becomes 2:3.find the fraction.

Answer 1

Let the numerator and denominator be x and y respectively. So the fraction will be x/y.

Now,

x+y=2x+4

Or, y=2x+4-x

Or, y=x+4 ...........[1]

Now,

x+3/y+3=2/3........[2]

Now, substituting the velue of 'y' from [1] into [2]

x+3/(x+4)+3=2/3

=>x+3/7+x=2/3

=>3x+9=14+2x

=>3x-2x=14-9

=>x=5

Now that we have found out 'x', we can put its value in [1] to get 'y'.

y=5+4=9

y=9

The fraction is 5/9

*hope its helpful*