Question

220 =
4) 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:

Let the numerator be x

Let the denominator be 2x+4

According to question:-we have

12(x-6)=2x+4-6

12x-72=2x-2

12x-2x=-2+72

10x=70

x=7

Numerator=7

Denominator=2x+4

2×7+4

14+4=18

Fraction=Numerator/Denominator

7/18

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Answer 2

Answer:

$\boxed{\sf\:The\:required\:fraction\:is\:\frac{7}{18}}$

Step-by-step-explanation:

Let the numerator of the fraction be x

And its denominator be y.

From the first condition,

$\sf\:y\:=\:2x\:+\:4\\\\\therefore\sf\:2x\:+\:4\:=\:y\\\\\therefore\sf\:2x\:-\:y\:=\:-\:4\:\:\:-\:-\:-\:(\:1\:)$

If 6 is subtracted both from the numerator and the denominator, then the numerator becomes ( x - 6 ) and the denominator becomes ( y - 6 ).

From the second condition,

$\sf\:y\:-\:6\:=\:12\:(\:x\:-\:6\:)\\\\\implies\sf\:y\:-\:6\:=\:12x\:-\:72\\\\\implies\sf\:12x\:-\:72\:=\:y\:-\:6\\\\\implies\sf\:12x\:-\:y\:=\:-\:6\:+\:72\\\\\implies\sf\:12x\:-\:y\:=\:66\:\:\:-\:-\:-\:(\:2\:)$

By subtracting equation ( 1 ) from equation ( 2 ), we get,

$\sf\:12x\:-\:\cancel{y}\:=\:66\:\:\:-\:-\:(\:2\:)\\\sf\:-\:\\\\\sf\:2x\:-\:\cancel{y}\:=\:-\:4\:\:\:-\:-\:-\:(\:1\:)\\\\\implies\sf\:10x\:=\:70\\\\\implies\sf\:x\:=\:\cancel{\frac{70}{10}}\\\\\implies\boxed{\red{\sf\:x\:=\:7}}$

Substituting x = 7 in equation ( 1 ), we get,

$\sf\:2x\:-\:y\:=\:-\:4\:\:\:-\:-\:(\:1\:)\\\\\implies\sf\:2\:\times\:7\:-\:y\:=\:-\:4\\\\\implies\sf\:14\:-\:y\:=\:-\:4\\\\\implies\sf\:-\:y\:=\:-\:4\:-\:14\\\\\implies\sf\:\cancel{-}\:y\:=\:\cancel{-}\:18\\\\\implies\boxed{\red{\sf\:y\:=\:18}}$

The numerator of the fraction ( x ) = 7

The denominator of the fraction ( y ) = 18

$\boxed{\sf\:The\:required\:fraction\:is\:\frac{7}{18}}$