Question

the denominator of a fraction is 1 less than the twice of the numerator if the numerator and denominator are both increased by 1 the fraction will become 3/5 find the fraction​

Answer 1

$\huge{\bold{\underline{\red{Given :}}}}$

• The denominator of a fraction is 1 less than the twice of the numerator .
• If the numerator and denominator both are increased by 1 then the fraction becomes 3/5.

$\huge{\bold{\underline{\red{To \ Find :}}}}$

• The Fraction

$\huge{\bf{\underline{\red{Solution :}}}}$

⇒Suppose the numerator be x

So, the denominator becomes y =  (2x - 1)

According to Question :

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

$\implies \bold{5(x +1) = 3(y +1)}$

$\implies \bold{5x + 5 = 3y + 3}$

$\implies \bold{ 5x - 3y = 3 - 5}$

Put the value of y :-

$\implies \bold{5x - 3( 2x -1) = -2}$

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

$\implies \bold{ - x = - 2 - 3}$

$\implies \boxed{\bold{ x = 5}}$

Now The fraction :-

$\implies \bold{\frac{x}{2x -1}}$

$\implies \bold{\frac{5}{10 - 1}}$

$\implies \boxed{\bold{\red{\frac{5}{9}}}}$

$\rule{200}2$