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 9/4.Find the original fraction.​

Answer 1

Answer:

24/14

Step-by-step explanation:

24/14

24+3=27

14-2=12

27/12=9/4

Answer 2

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 9/4. Find the original fraction.

Answer :-

Fraction is 15/10.

Explanation :-

Ratio of numerator and denominator of the fration = 3 : 2

Let the numerator be 3x and denominator be 2x

Given

If 3 is added to the numerator and 2 is subtracted from the denominator = 9/4

⇒ (3x + 3)/(2x - 2) = 9/4

By cross multiplication

⇒ 4(3x + 3) = 9(2x - 2)

⇒ 12x + 12 = 18x - 18

⇒ 12 + 18 = 18x - 12x

⇒ 30 = 6x

⇒ 30/6 = x

⇒ 5 = x

⇒ x = 5

Numerator of the fraction = 3x = 3(5) = 15

Denominator of the fraction = 2x = 2(5) = 10

Fraction = 3x/2x = 15/10

∴ the fraction is 15/10.