Question

The denominator of a fraction is greater than its numerator by 4. If the numerator is increased by 7 and denominator is decreased by 2 ,the new fraction obtained is 6/5. Find the original fraction.



▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

❒ Use Latex to give the answer.
❒ No Spams.
❒ Thank you. ​

Answer 1

→ Let the numerator be x and the denominator be x+4.

Hence ,the fraction is $\frac{x}{x + 4}$ . ... ..(i)

According to the Question,

$\frac{x + 7}{x + 4 - 2} = \frac{6}{5} \\ \\ \frac{x + 7}{x + 2} = \frac{6}{5} \\ \\ 5x + 35 = 6x + 12 \\ \\ 35 - 12 = 6x - 5x \\ \\ 23 = x \\ \\ x = 23$

Putting the value of x in equation (i) :

$\frac{x}{x + 4} = \frac{23}{23 + 4 } \\ \\ = \frac{23}{27}$

Therefore, the required fraction is 23/27.

Answer 2

Answer :

The original fraction is $\sf \dfrac{23}{27}$

Step by Step Explanation :

Let for the original fraction ;

• Numerator be = x

As per the given condition - Denominator of the fraction is greater than and it's numerator by 4 therefore,

• Denominator must be = x + 4

By Numerator and Denominator ,

Original Fraction is : $\rm\dfrac{x}{x+ 7}$

$\large \bigstar$ When the numerator is increased by 7 and denominator is decreased by 2 ;

Fraction becomes : $\rm \dfrac{(x) + 7}{(x + 4) - 2}$

Therefore,

New Fraction is : $\rm\dfrac{x + 7}{x + 2}$

$\large \dashrightarrow$ According To Question ;

$\Large \dag \large \: \: \: \underline{ \boxed{ \bf \frac{x + 7}{x + 2} = \frac{6}{5} }}$

➡️ On cross multiplication :

$\\ :\longmapsto \rm 5(x + 7) = 6(x + 2)$

$:\longmapsto \rm 5x + 35 = 6x + 12$

$:\longmapsto \rm 5x - 6x = 12 - 35$

$:\longmapsto \rm \cancel - x = \cancel - 23$

$\red{:\longmapsto \bf \underbrace{\underline{ \blue{x = 23 }}}}$

As we assumed numerator as x so,

Numerator of original fraction = 23

As per the question denominator of the fraction is greater than and it's numerator by 4

$\therefore \:$ Denominator = 23 + 4

Hence,

Denominator of original fraction = 27

Therefore,

Original Fraction is : $\sf \dfrac{23}{27}$