Question

the denominator of a fraction is 4 more than the numerator if 1 is added to the numerator rater and 2 is added to the denominator the value of the functions become 4/5 find the original fraction
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Answer 1

Correct Question :

The denominator of a fraction is 4 more than the numerator if 1 is added to the numerator and 2 is added to the denominator the value of the fractions become 4/5 find the original fraction

Given :

• Denominator of a fraction is 4 more than numerator

• Adding 1 to numerator and 2 to denominator the value of the fraction equals 4/5

To Find :

• The orginal fraction

Solution :

Let the numerator of the fraction be 'x'

Then the denominator becomes 'x + 4 ' [ Since denominator is 4 more than numerator]

Denominator when 2 is added to it is ' x + 6 '

Numerator when 1 is added to it is ' x + 1 '

$\dag\boxed{\rm{Fraction\:=\:\dfrac{Numerator}{Denominator}}}$

According to the question ,

$\rm \dfrac{x + 1}{x + 6} = \dfrac{4}{5}$

By cross multiplication ,

$: \implies \rm6(x + 1) = 4(x + 6) \\ \\ : \implies \rm \: 5x + 5 = 4x + 24 \\ \\ : \implies \rm \: 5x - 4x= 24 - 5\\ \\ : \implies \rm \: x = 19 \: \bigstar$

Numerator = x = 19

Denominator = x + 4 = 23

$: \implies \rm \: fraction = \dfrac{numerator}{denominator} \\ \\ : \implies \rm \: fraction = \dfrac{19}{23} \: \: \bigstar$

∴ The required fraction is 19/23

Verfication :

If numerator is 19 and denominator is 23 ,

(i) Denominator when 2 is added to it becomes 25

(ii) Numerator when 1 is added to it becomes 20

Fraction = 20/25 = 4/5

The value mentioned in question is also 4/5

Since , all the conditions are satisfied , The required fraction is 19/23

Answer 2

Answer:

Correct Question :

The denominator of a fraction is 4 more than the numerator if 1 is added to the numerator and 2 is added to the denominator the value of the fractions become 4/5 find the original fraction

Given :

Denominator of a fraction is 4 more than numerator

Adding 1 to numerator and 2 to denominator the value of the fraction equals 4/5

To Find :

The orginal fraction

Solution :

Let the numerator of the fraction be 'x'

Then the denominator becomes 'x + 4 ' [ Since denominator is 4 more than numerator]

Denominator when 2 is added to it is ' x + 6 '

Numerator when 1 is added to it is ' x + 1 '

\dag\boxed{\rm{Fraction\:=\:\dfrac{Numerator}{Denominator}}}†

Fraction=

Denominator

Numerator

According to the question ,

\rm \dfrac{x + 1}{x + 6} = \dfrac{4}{5}

x+6

x+1

=

5

4

By cross multiplication ,

\begin{gathered} : \implies \rm6(x + 1) = 4(x + 6) \\ \\ : \implies \rm \: 5x + 5 = 4x + 24 \\ \\ : \implies \rm \: 5x - 4x= 24 - 5\\ \\ : \implies \rm \: x = 19 \: \bigstar\end{gathered}

:⟹6(x+1)=4(x+6)

:⟹5x+5=4x+24

:⟹5x−4x=24−5

:⟹x=19★

Numerator = x = 19

Denominator = x + 4 = 23

\begin{gathered} : \implies \rm \: fraction = \dfrac{numerator}{denominator} \\ \\ : \implies \rm \: fraction = \dfrac{19}{23} \: \: \bigstar\end{gathered}

:⟹fraction=

denominator

numerator

:⟹fraction=

23

19

★

∴ The required fraction is 19/23

Verfication :

If numerator is 19 and denominator is 23 ,

(i) Denominator when 2 is added to it becomes 25

(ii) Numerator when 1 is added to it becomes 20

Fraction = 20/25 = 4/5

The value mentioned in question is also 4/5

Since , all the conditions are satisfied , The required fraction is 19/23