Question

The numerator and the denominator of a fraction are inthe ratio 3:2 . If the is added to the numerator and 2 is subtracted from the denominator,anew fraction is formed whose value is 9/4.Find the original fraction.

Answer 1

hey here is your answer

given that numerator and denominator are in the ratio of 3:2

so , numerator = 3x

denominator = 2x

and also they said in the question that 3 is added to the numerator and 2 is subtracted from the denominator so the equation becomes like this,

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

cross multiply

⇒4 (3x+3) = 9(2x-2)

⇒ 12x+12= 18x -18

⇒18x-12x= 12+18

6x= 30

x= $\frac{30}{6} = 5$

subsituite the value of x in the numbers

here fraction=$\frac{3x}{2x}$

$\frac{3*5}{2*5}$

⇒ $\frac{3}{2}$⇒ is the answer

hope it helps

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