Question

The denominator of a fraction is 1 less than
twice its numerator. If 1 is added to
numerator and denominator respectively,
the ratio of numerator to denominator is
3:5. Find the fraction.​

Answer 1

Answer:

Let the numerator be x.

Then, the denominator (2x-1)

Atq,

$\: \: \: \: \frac{x + 1}{(2 x- 1) + 1} = \frac{3}{5} \\ = > \frac{x + 1}{2x -1 + 1 } = \frac{3}{5} \\ = > \frac{x + 1}{2x} = \frac{3}{5} \\ = > 5(x + 1) = 2x \times 3 \\ = > 5x + 5 = 6x \\ = > 5x - 6x = - 5 \\ = > -x = - 5 \\ = > x = 5$

Hence, Numerator $= 5$

Denominator

$= (2 \times 5 - 1)$

$= 10-1$ = 9

$Fraction = \frac{5}{9}$