Question

the numerator and denominator of a fraction are in the ratio 3:2 if 3 is added to the numerator and 2 is subtracted from the denominator, fraction 9/4 is obtained find the numerator and denominator of orginal fraction​

Answer 1

Answer:

15/10

Step-by-step explanation:

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

Cross multiply

18x - 18 = 12x + 12

18x - 12x = 18 + 12

6x = 30 ⇒ x = 5

$\frac{15}{10}$

Answer 2

Given :

• Numerator and Denominator of a fraction are in ratio 3:2.
• If 3 is added to the numerator and 2 is subtracted from the denominator, the fraction becomes 9/4.

To Find :

• Numerator and Denominator of the fraction.

Solution :

$\longmapsto\tt{Let\:Numerator\:be=3x}$

$\longmapsto\tt{Let\:Denominator\:be=2x}$

Now ,

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

$\longmapsto\tt{Numerator=3x+3}$

$\longmapsto\tt{Denominator=2x-2}$

A.T.Q :

$\longmapsto\tt{\dfrac{3x+3}{2x-2}=\dfrac{9}{4}}$

$\longmapsto\tt{4(3x+3)=9(2x-2)}$

$\longmapsto\tt{12x+12=18x-18}$

$\longmapsto\tt{12x-18x=-18-12}$

$\longmapsto\tt{-6x=-30}$

$\longmapsto\tt{x=\cancel\dfrac{-30}{-6}}$

$\longmapsto\tt\bold{x=5}$

Value of x is 5..

Therefore :

$\longmapsto\tt{Numerator=3(5)}$

$\longmapsto\tt\bold{15}$

$\longmapsto\tt{Denominator=2(5)}$

$\longmapsto\tt\bold{10}$

Therefore , The original fraction is 15/10...