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. Find the fraction.

Answer 1

Answer:

let numerator be x

and denominator be y

y=4+2x

2x-y+4=0-->(1)

when 6 is decreased from both numerator and denominator,

(y-6)=12(x-6)

y-6=12x-72

12x-y-72+6=0

12x-y-66=0-->(2)

now solve (1) and (2)

(1)--> 2x -y+4=0

(2)-->12x-y-66=0

-10x +70=0

-10x=-70

x=7

then substitute x=7 in equation(1),to get y

(1)-->2x-y+4=0

14-y+4=0

-y=-18

y=18

therefore,the fraction x/y is 7/18.

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption :-

Numerator be p

Also,

Denominator be t

So,

Fraction = p/t

So,

⇒ t = 2p + 4

⇒ 2p - t + 4 = 0

Situation :-

⇒ t - 6 = 12(p - 6)

⇒ t - 6 = 12p - 72

⇒ 12p - t - 66 = 0

From above we get two equations :-

⇒ 2p - t + 4 = 0 ............... (1)

⇒ 12p - t - 66 = 0 .............(2)

Now

Subtract (1) from (2),

⇒ 10p - 70 = 0

⇒ p = 7

Now,

Substitute value of p in (1),

⇒ 14 - t + 4 = 0

⇒ t = 18

Therefore,

Fraction = 7/18