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 . Find the original
fraction

Answer 1

Answer:

Correct 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.

Solution:-

Let numerator of the fraction = 3x

and

Denominator of the fraction = 2x

( since, they are in ratio 3:2)

According to the question ;

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

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

=> 12x + 12 = 18x -18

=> 18x -12x = 12 +18

=> 6x = 30

=> x = 5

Thus,

The Original fraction = 3x/2x

= 3•5/2•5

= 15/10

Hence, the required fraction is 15/10.

Answer 2

Correct 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 :-

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.