Question

the numerator and the denominator of a fraction is in the ratio 3:2. if three is added to the numerator and two is subtracted from the denominator, its value becomes 9/4. what is the value of the original fraction?

Answer 1

Hey.

let the fraction be 3x/2x

so, a/q
if (3x+3)/(2x-2) =9/4
so, 12x+12=18x-18
or, 18x-12x=12+18
or, 6x=30
so, x=5
fraction is 3×5/2×5=15/10

thanks.

Answer 2

hiii...

Let numerator be X
and denominator be Y.

according to the question,

fraction is in the form of 3:2

3X/2Y

if three is added to numerator and two is subtracted from denominator.then,

3x+3/2y-3=9/4

4(3x+3)=9(2y-2)

12x+12=18y-18

12x-18y+30=0

4x-6y+10=0

2x-3y+5=0.
by factorization,

we get -5/2,5/2

therefore x=5/2

substitute in equation -------------(1)


2x-3y+10=0

2(5/2)-3y+10=0

5-3y=-10

-3y=-15

y=5..

fraction x/y,=

5/2/5

1/2

the original fraction is 1/2