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

Answer 1

Let Numerator=x
Then Denominator is 4 more than 2 times the Numerator.
Denominator=2x+4
Fraction=$\frac{x}{2x+4}$
Now if 6 is Decreased From Both . Fraction become
Numerator=x-6
Denominator=2x+4-6=2x-2
Fraction=$\frac{x-6}{2x-2}$

A/Q
New Denominator=12×New Numerator
➡️2x-2=12(x-6)
➡️2x-2=12x-72
➡️2x-12x=-72+2
➡️-10x=-70. (- -=+)
➡️x=70/10
➡️x=7

Original Numerator=x=7
Original Denominator=2x+4=2×7+4=18
Original Fraction=$\frac{7}{18}$

$\boxed{\mathbf{Fraction=\frac{7}{18}}}$