Question

The denominator of a fraction is greater than its numerator by 12. If the numerator is decreased by 2 and the denominator is increased by 7, the new fraction is equivalent to 1/2. find the fraction.

Answer 1

Solution :

Let the numerator of the fraction = x

denominator = ( x + 12 )

Now , the fraction = x/( x + 12 ) ----( 1 )

If the numerator is decreased by 2 ,

and the denominator is increased

by 7 , then the fraction is equivalent

to 1/2 .

( x - 2 )/( x + 12 + 7 ) = 1/2

=> ( x - 2 )/( x + 19 ) = 1/2

=> 2( x - 2 ) = x + 19

=> 2x - 4 = x + 19

=> 2x - x = 19 + 4

=> x = 23

Therefore ,

Required fraction = x/( x + 12 )

= 23/( 23 + 12 )

= 23/35

•••••

Answer 2

Answer:

23/35

Step-by-step explanation:

Let x be the numerator and y be the denominator.

Hence, the fraction is x/y.

(i)

Denominator of a fraction is greater than its numerator by 12.

y = x + 12.

(ii)

Numerator is decreased by 2 and the denominator is increased by 7, the fraction is 1/2.

⇒ (x - 2)/(y + 7) = 1/2

⇒ 2x - 4 = y + 7

⇒ 2x - y = 11

Substitute (i) in (ii), we get

⇒ 2x - y = 11

⇒ 2x - [x + 12] = 11

⇒ 2x - x - 12 = 11

⇒ x = 23

Substitute x = 23 in (i), we get

⇒ y = 23 + 12

⇒ y = 35.

Therefore, the required fraction is 23/35.

Hope it helps!