Question

The denominator of a fraction is 4 more
than twice its numerator. If 6 is subtracted
from both the numerator and the denomina-
tor, the denominator becomes 12 times
the numerator. Find the fraction.​

Answer 1

Solution :-

Let the numerator and the denominator

be x and y

Therefore , Fraction = x / y

According to the question ,

Denominater = 2 ( x ) + 4

Y = 2x + 4

Therefore ,

2x - y + 4 = 0 ......eq( 1 )

Now , According to the question if 6 is subtracted from both the numerator and the denominator then the denominator becomes 12 times the numerator .

y - 6 = 12( x - 6 )

y - 6 = 12x - 72

12x - y -72 + 6 = 0

12x - y - 66 = 0 ............eq( 2 )

Now , subtracting equation 1 from 2

12x - y - 66 - ( 2x - y + 4 )

12x - y -66 - 2x + y - 4

10x - 70

10x = 70

x = 70/10

x = 7

Putting the value of x in eq( 1 )

2x - y + 4

2( 7) - y = -4

14 - y = -4

-y = -4 - 14

y = 18

Hence , The required fraction

is 7 / 18

Answer 2

Hey mate,

The required fraction will be 7/18 .

Hope it helps.