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.

Given:

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.

 To do:

We have to find the original fraction.

Solution:

Let the numerator and denominator of the original fraction be $x$ and $y$ respectively.

The original fraction$=\frac{x}{y}$

According to the question,

$y=2x+4$.....(i)

When the numerator and denominator are decreased by 6, the denominator becomes 12 times the numerator.

The new numerator $=x-6$

The new denominator $=y-6$

$\Rightarrow y-6=12\times(x-6)$

$y-6=12x-72$

$12x-72+6=y$

$12x-72+6=2x+4$         [From (i)]

$12x-2x=4+66$

$10x=70$

$x=\frac{70}{10}$

$x=7$

$\Rightarrow y=2x+4=2(7)+4=14+4=18$.

Therefore, the original fraction is $\frac{7}{18}$.    

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Updated on: 10-Oct-2022

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