Question

The denominator of a fraction is 1 more
than twice its numerator If 1 is
added to the numerator and the denominator
, the ratio of the numerator to
the denominator is 1:2 find the
fraction









​

Answer 1

SOLUTION :-

Let,

Numerator = x

Denominator = y

According to the first condition,

$\longrightarrow\sf y = 2x+1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..........................(1)$

According to the second condition,

$\longrightarrow\sf \dfrac{x+1}{y+1}=\dfrac{1}{2}\\\\\longrightarrow\sf 2(x+1)=y+1\\\\\longrightarrow 2x+2 = y+1 \\\\\longrightarrow 2x-y = -1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..............................(2)$

There are infinite values for x and y that will satisfy the above conditions.

One of the two possible values are :

$\bullet\sf \ \dfrac{4}{9}$

 Verification,

  $\longrightarrow \sf 2\times4 - 9\\\\\longrightarrow 8-9 \\\\\longrightarrow -1$

$\bullet\sf \ \dfrac{8}{17}$

  Verification,

   $\longrightarrow\sf 2\times 8 - 17 \\\\\longrightarrow 16-17 \\\\\longrightarrow -1$