Question

The denominator of a fraction is 1 more than twice its numerator. If the numerator and denominator are both increased by 5 ,it becomes 3/5. Find tha original fraction.

Answer 1

Let the numerator be x and the denominator is 2x+1
then
x+5/$\frac{x+5}{2x+6}$=3/5
then  x=7 and the fraction is7/15

Answer 2

Answer:

$Original\: fraction=\frac{7}{15}$

Step-by-step explanation:

Let the numerator = x

Denominator = 2x+1

$Original \: fraction =\frac{x}{2x+1}---(1)$

According to the problem given,

If the numerator and denominator are both increased by 5 ,it becomes 3/5.

$\implies \frac{x+5}{2x+1+5}=\frac{3}{5}$

$\implies \frac{x+5}{2x+6}=\frac{3}{5}$

$\implies 5(x+5)=3(2x+6)$

$\implies 5x+25=6x+18$

$\implies 25-18=6x-5x$

$\implies 7 = x$

$\implies x = 7$

Substitute x=7 in (1), we get

$Original \: fraction \\= \frac{7}{2\times 7+1}\\=\frac{7}{15}$

Therefore,

$Original \: fraction \\=\frac{7}{15}$

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