Question

The numerator and the denominator of a fraction are in the ratio 3:2. If 3 is added to the numerator and 2 is subtracted from the denominator, a new fraction is formed who's value is 9/4. Find the original fraction

Answer 1

Answer:

3/2

Step-by-step explanation:

numerator and the denominator of a fraction are in the ratio 3:2.

and

If 3 is added to the numerator and 2 is subtracted from the denominator, a new fraction is formed whose value is 9/4.

solution:-

let numerator of fraction = 3x

and

denominator = 2x

( because they are in ratio 3:2)

According to 2nd condition ;

=>( 3x + 3 ) / (2x - 2) = 9/4

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

=> 12x + 12 = 18x -18

=> 18x -12x = 12 +18 = 30

=> 6x = 30

=>x = 5

here,

the Original fraction = 3x / 2x

=> 3×5 / 2 ×5

=> 3/2 answer

Answer 2

Answer:

The original fraction is $\frac{3}{2}$ .

Step-by-step explanation:

Given -

The numerator and the denominator of a fraction are in the ratio 3:2.

If 3 is added to the numerator and 2 is subtracted from the denominator, a new fraction is formed who's value is 9/4.

To find -

The original fraction

Solution -

Let, the original fraction is $\frac{3x}{2x}$

As,

3 is added to the numerator and 2 is subtracted from the denominator, a new fraction is formed who's value is 9/4. write it as,

$\frac{3x+3}{2x-2} = \frac{9}{4}$

First we have to find the value of x to get the original fraction value.

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

$12x+12= 18x-18$

$12x-18x = -18-12\\-6x=-30$

Divide both side by (-6) we get,

$x=5$

put the value of x in original fraction

$\frac{3x}{2x} =\frac{3\times 5}{2\times 5}=\frac{15}{10}$

Divide by 5 we get

= $\frac{3}{2}$

∴ The original fraction is $\frac{3}{2}$ .