Question

find the fraction whose numerator is 4 less than the denominator. if 1 is subtracted from numerator and 3 is added to the denominator, fraction becomes 1/5.find the original fraction​

Answer 1

Answer:

• The original fraction is 3/7.

Step-by-step explanation:

Let us assume:

• Numerator of a fraction be x.

Given that:

• Numerator is 4 less than the denominator.
• Then, Denominator of a fraction = (x + 4)

• 1 is subtracted from numerator and 3 is added to the denominator, fraction becomes 1/5.

⇒ (x - 1)/(x + 4 + 3) = 1/5

To Find:

• The original fraction.

Finding the original fraction:

• According to the question.

⇒ (x - 1)/(x + 4 + 3) = 1/5

• Cross multiplication.

⇒ 5(x - 1) = 1(x + 4 + 3)

⇒ 5x - 5 = x + 4 + 3

⇒ 5x - 5 = x + 7

⇒ 5x - x = 7 + 5

⇒ 4x = 12

⇒ x = 12/4

⇒ x = 3

We get,

• Numerator = x = 3
• Denominator = x + 4 = 3 + 4 = 7

Original fraction = Numerator/Denominator

Original fraction = 3/7

Answer 2

$\huge\blue{\tt \: Answer - }$

$\begin{gathered}\begin{gathered}\bf \: Let - \green{\begin{cases} &\tt{denominator \: = x} \\ &\sf{numerator \: = \: x - 4} \end{cases}}\end{gathered}\end{gathered}$

So,

$\begin{gathered}\begin{gathered}\bf \:fraction - \purple{\begin{cases} &\bf{\dfrac{x - 4}{x} }  \end{cases}}\end{gathered}\end{gathered}$

$\large \underline{\tt \: \red{ According \: to \: statement }}$

• if 1 is subtracted from numerator and 3 is added to the denominator, fraction becomes 1/5.

Now,

$\rm :\implies\:Numerator = x - 4 - 1 = x - 5$

$\rm :\implies\:Denominator = x + 3$

So,

$\begin{gathered}\begin{gathered}\bf \:fraction - \pink{\begin{cases} &\bf{\dfrac{x - 5}{x + 3} }  \end{cases}}\end{gathered}\end{gathered}$

$\large \underline{\tt \: \blue{ According \: to \: statement }}$

$\rm :\implies\:\dfrac{x - 5}{x + 3} = \dfrac{1}{5}$

$\rm :\implies\:5x - 25 = x + 3$

$\rm :\implies\:5x - x = 25 + 3$

$\rm :\implies\:4x = 28$

$\rm :\implies\: \boxed{ \green{ \bf \:x = 7 }}$

$\begin{gathered}\begin{gathered}\bf So,\:fraction - \green{\begin{cases} &\tt{\dfrac{x - 4}{x} =\dfrac{7 - 4}{7} = \dfrac{3}{7} }  \end{cases}}\end{gathered}\end{gathered}$