Question

The denominator of a fraction is 4 more than twice its numerator. Denominator
becomes 12 times the numerator, if both the numerator and the denominator are
reduced by 6. Find the fraction.​

Answer 1

Answer:

$\red \bigstar \sf The\: required \: fraction\: is \: \dfrac{7}{18}$

 SOLUTION  

$\sf Let \:us \:assume\: that\: the \:fraction\: is \: \dfrac{x}{y}$

It is said that  denominator is 4 more than twice its numerator.

$\implies$ y = 2x + 4

$\implies$ 2x − y + 4 = 0$\longrightarrow(1)$

It is also told in the question that  Denominator becomes 12 times the numerator, if both the numerator and the denominator are reduced by 6.

$\implies$ y − 6 = 12 (x−6)

$\implies$ y − 6 = 12 x − 72

$\implies$ 12x − y − 66 = 0 $\longrightarrow(2)$

Let the solve (1) and (2) , by subtracting (1) from (2)

 12x − y − 66 = 0

- 2x + y -     4 =  0

10x       - 70     = 0

10x - 70 = 0

10x = 70

$\sf x= \dfrac{70}{10} = 7$

Now let us find the value of 'y' by substituting value of 'x' as 7 in (1)

$\implies$

2 × 7 - y + 4

$\implies$

14 - y + 4 = 0

$\implies$

18 - y = 0

$\implies$

-y = -18

Therefore the value of 'y' = 18

$\sf The \: required\: Fraction\: is \:of \:the \:form \: \dfrac{x}{y}$

$\bigstar \sf Therefore\: the\: required\: fraction\: is \: \dfrac{7}{18}$