Question

The sum of numerator and denominator of a fraction is 8.If 3 is added to both the numerator nad denominator the fraction becomes 3/4.Find the fraction

Answer 1

As the sum of the numerator and the denominator of a fraction is 8, we can take the numerator and denominator as x and 8 - x respectively or vice versa.

Here the numerator and the denominator are taken as x and 8 - x respectively.

$\dfrac{x}{8-x}$

Given that the fraction becomes 3/4 if 3 is added to both the numerator and the denominator each.

$\begin{aligned}&\dfrac{x+3}{8-x+3}&=&\ \ \dfrac{3}{4}\\ \\ \Longrightarrow\ \ &\dfrac{x+3}{11-x}&=&\ \ \dfrac{3}{4}\\ \\ \Longrightarrow\ \ &4(x+3)&=&\ \ 3(11-x)\\ \\ \Longrightarrow\ \ &4x+12&=&\ \ 33-3x\\ \\ \Longrightarrow\ \ &4x+3x&=&\ \ 33-12\\ \\ \Longrightarrow\ \ &7x&=&\ \ 21\\ \\ \Longrightarrow\ \ &x&=&\ \ \Large \textbf{3}\end{aligned}$

Hence the value of x is 3. Thus the numerator is 3.

$8-x\ =\ 8-3\ =\ \Large \textbf{5}$

Hence the denominator is 5.

Thus the fraction is 3/5.

Answer 2

Answer :-

Let the numerator be x.

As sum of numerator & denominator is 8, So,

Denominator = 8 - x

Fraction = $\dfrac{x}{8 - x}$

According To Question :-

=> $\dfrac{x + 3}{8 - x + 3}$ = $\dfrac{3}{4}$

=> $\dfrac{x + 3}{11 - x}$ = $\dfrac{3}{4}$

By cross- multiplication,

=> 4(x + 3) = 3(11 - x)

=> 4x + 12 = 33 - 3x

=> 4x + 3x = 33 - 12

=> 7x = 21

x = $\dfrac{21}{7}$

x = 3

So, the numerator is 3 ;

Denominator = 8 - 3 = 5

Thus, the fraction is :-

=> $\dfrac{3}{5}$