Question

The denominator of a fraction is 4 more than twice the numerator. when both the numerator and denominator are decreased by 6, then the denominator becomes 12 times the numerator. Determine the fraction.​

Answer 1

Answer:

Let the numerator and denominator of the fraction be x and y respectively. Then,

Fraction =

y

x

It is given that

Denominator =2 (Numerator) +4

⇒y=2x+4

⇒2x−y+4=0

According to the given condition, we have

y−6=12(x−6)

⇒y−6=12x−72

⇒12x−y−66=0

Thus, we have the following system of equations

2x−y+4=0 .(i)

12x−y−66=0 ..(ii)

Subtracting equation (i) from equation (ii), we get

10x−70=0

⇒x=7

Putting x=7 in equation (i), we get

14−y+4=0

⇒y=18

Hence, required fraction =

18

7