Question

The numerator of a fraction is 3 less than the denominator.If both the numerator and denominator are increased by 2.find the original fraction​

Answer 1

Correct Question :

The numerator of a fraction is 3 less than the denominator.If both the numerator and denominator are increased by 2 , then the fraction obtained is 6/7 .Find the original fraction .

Given :

• Numerator of a fraction is 3 less than the denominator.
• If both the numerator and denominator are increased by 2 , then the fraction obtained is 6/7 .

To Find :

• The original fraction .

Solution :

$\longmapsto\tt{Let\:Denominator\:be=x}$

As Given that Numerator of a fraction is 3 less than the Denominator. So ,

$\longmapsto\tt{Numerator=x-3}$

Now ,

• If both the numerator and denominator are increased by 2 , then the fraction obtained is 6/7 .

$\longmapsto\tt{Denominator=x+2}$

$\longmapsto\tt{Numerator=x-3+2}$

A.T.Q :

$\longmapsto\tt{\dfrac{x-3+2}{x+2}=\dfrac{6}{7}}$

$\longmapsto\tt{7(x-3+2)=6(x+2)}$

$\longmapsto\tt{7x-21+14=6x+12}$

$\longmapsto\tt{7x-7=6x+12}$

$\longmapsto\tt{7x-6x=12+7}$

$\longmapsto\tt\bf{x=19}$

Value of x is 19 ...

Therefore :

$\longmapsto\tt{Numerator=19-3}$

$\longmapsto\tt\bf{16}$

$\longmapsto\tt\bf{Denominator=19}$

So , The Original Fraction is 16/19 ....

Answer 2

Answer:

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★16/19

Correct Question

• The numerator of a fraction is 3 less than the denominator. if both the numerator and denominator are increased by 2,the new fraction becomes 6/7.Find the original fraction?

Solution

★Let the denominator of the fraction be X.

★Then the numerator of the fraction = (X-3)

★Fraction = Numerator/Denominator = X-3/X.

★Numerator and denominator are increased by 2 then the Numerator and denominator becomes (X-3+2) and (X+2).

★Fraction = Numerator/Denominator =(X-3+2)/(X+2).

★According to question,

• (X-3+2)/(X+2) = 6/7

• X-1/X+2 = 6/7

• 7(X-1) = 6(X+2)

• 7X-7 = 6X+12

• 7X-6X= 12+7

• X = 19

★Therefore

• Numerator = (X-3) = (19-3) = 16

• And,

• Denominator =(X) = 19

★Therefore,

• Original Fraction = Numerator/Denominator

• =(X-3)/X

• = 16/19

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