Question

The numerator of fraction is 2 less than the denominator . if one is added to the denominator the fraction becomews 1\2 find the fraction

Answer 1

Answer:-

$\sf{The \ fraction \ is \ \frac{3}{5}.}$

Given:

• The numerator of fraction is 2 less than the denominator.

• If one is added to the denominator the fraction becomews 1\2.

To find:

• The fraction.

Solution:

$\sf{Let \ the \ numerator \ of \ the \ fraction \ be \ x}$

$\sf{and \ it's \ denominator \ be \ y.}$

$\sf{According \ to \ the \ first \ condition.}$

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

$\sf{According \ to \ the \ second \ condition.}$

$\sf{\frac{x}{y+1}=\frac{1}{2}}$

$\sf{\therefore{2x=y+1}}$

$\sf{\therefore{2x-y=1...(2)}}$

$\sf{Subtract \ equation (1) \ from \ equation (2), \ we \ get}$

$\sf{2x-y=1}$

$\sf{-}$

$\sf{x-y=-2}$

_________________

$\boxed{\sf{\therefore{x=3}}}$

$\sf{Substitute \ x=3 \ in \ equation (1)}$

$\sf{3-y=-2}$

$\sf{\therefore{-y=-2-3}}$

$\sf{\therefore{-y=-5}}$

$\boxed{\sf{\therefore{y=5}}}$

$\sf{The \ fraction \ is \ \frac{x}{y}=\frac{3}{5}}$

$\sf\purple{\tt{\therefore{The \ fraction \ is \ \frac{3}{5}.}}}$

Answer 2

✯✯ QUESTION ✯✯

The numerator of fraction is 2 less than the denominator . if one is added to the denominator the fraction becomews 1\2 find the fraction

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✰✰ ANSWER ✰✰

$\implies\tt{Let\:the\:denominator\:be=x}$

➮As Given that numerator of fraction is 2 less than the denominator.So ,

$\implies\tt{Numerator=x-2}$

➥A.T.Q : -

➮If one is added to the denominator the fraction becomews 1/2 find the fraction.So,

$\implies\tt{\dfrac{x-2}{x+1}=\dfrac{1}{2}}$

$\implies\tt{1(x-1)=2(x-2)}$

$\implies\tt{x+1=2x-4}$

$\implies\tt{x-2x=-4-1}$

$\implies\tt{-1x=-5}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{x}\orange{=}\purple{5}}}$

➥Now ,

$\implies\tt{Numerator=x-2}$

$\implies\tt{5-2}$

$\implies\tt\bold{3}$

$\implies\tt{Denominator=x}$

$\implies\tt\bold{5}$

☛So , The fraction is 3/5...