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 whose value is
$\frac{9}{4}$
Find the original fraction
​

Answer 1

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:-

Let the fraction be x/y .

Given:

Numerator and denominator are in the ratio 3 : 2

→ x : y = 3 : 2

→ x/y = 3/2

On cross multiplication we get,

→ 2x = 3y

→ x = (3y)/2 -- equation (1)

If 3 is added to numerator and 2 is subtracted from the denominator, the fraction becomes 9/4.

→ (x + 3) / (y - 2) = 9/4

→ 4(x + 3) = 9(y - 2)

→ 4x + 12 = 9y - 18

Putting the value of x from equation (1) we get,

→ 4(3y/2) + 12 = 9y - 18

→ 2(3y) + 12 = 9y - 18

→ 12 + 18 = 9y - 6y

→ 3y = 30

→ y = 30/3

→ y = 10

Substitute the value of y in equation (1)

→ x = 3(10)/2

→ x = 15

Hence, the required fraction x/y is 15/10.