Question

11 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 2. Find the original
fraction.​

Answer 1

Step-by-step explanation:

let the numerator denominator be x

original numerator = 3x

originaldenominator =2x

original fraction =3x/2x

new numerator = 3x+3

new denominator = 2x-2

new fraction = 3x+3 /2x-2

new fraction =2 ( given)

3x +3 / 2x-2 =2

3x +3 = 4x-4

4+3 = 4x -3x

7 =x

original numerator = 3x =3×7 =21

original denominator =2x =2×7 =14

original fraction = 21/14

Answer 2

Solution:-

Given that, numerator and the denominator of a fraction are in ratio of 3 : 2.

If 3 is added to the numerator and 2 is subtracted from the denominator the the new fraction is formed which value is 2.

Therefore,

Let the numerator be 3x and let the denominator be 2x ..........equation 1

Now,

: ⟹ ( 3x + 3 ) / ( 2x - 2 ) = 2

: ⟹ 3x + 3 = 2( 2x - 2 )

: ⟹ 3x + 3 = 4x - 4

: ⟹ 3x - 4x = -4 - 3

: ⟹ - x = - 7

( Cancelling minus from both sides )

: ⟹ x = 7 ............. equation 2

Therefore, the original fraction:-

Numerator is 3x and denominator of the fraction is 2x ........( from equation 1 )

: ⟹ ( 3 × 7 ) / ( 2 × 7 )

: ⟹ 21 / 14

Required Answer:-

The original fraction is 21/14.