Question

The denomi ator of a fraction is 1 more than twice its numerator . If the numerator and denominator are both increased by 5,it becomes three fifth .find the orignal fraction

Answer 1

Let numerator be x and denominator be ( 2x + 1 ) { According to the Question }


$=> \bold{Fraction = \frac{x}{2x + 1} }$




Given, when increased by 5, it becomes 3 / 5



$=> \frac{x + 5}{2x + 1+ 5} = \frac{3}{5} \\ \\ = > \frac{x + 5}{2x + 6} = \frac{3}{5} \\ \\ = > 5(x + 5) = 3(2x + 6) \\ \\ = > 5x + 25 = 6x + 18 \\ \\ = > 25 - 18 = 6x - 5x \\ \\ = > 7 = x \\ \\ \\ \\ \mathbf{Hence, \: \: Fraction \: \: is \frac{x}{2x+1}\: => \frac{7}{2(7)+1}\:=> \frac{7}{14+1}\:=> \frac{7}{15}}$

Answer 2

Hello dear,

Here is your answer,

Let the numerator of the fraction be x
(According to the question)
The denominator of the fraction is one more than twice it's numerator.

So, denominator = (2x+1)

Therefore,
fraction is,

$\frac{x}{2x + 1}$


Now,
When 5 is added to both numerator and denominator the fraction becomes three - fifth.

Therefore,

$\frac{x + 5}{2x + 1+ 5} = \frac{3}{5} \\ \\ = > \frac{x + 5}{2x +6} = \frac{3}{5} \\ \\ = > 5(x + 5) = 3(2x + 6) \\ \\ = > 5x + 25 = 6x + 18 \\ \\ = > 25 - 18 = 6x - 5x \\ \\ = > 7 = x$

Check,

$\frac{x + 5}{2x + 6} \\ \\ = > \frac{7 + 5}{2 \times 7 + 6} \\ \\ = > \frac{12}{20} = \frac{3}{5}$


Hope it helps.