Question

In a fraction , twice the numaratore is 2 more than the denomanator . If 3 is added to bothe of them the fraction becomes 2/3 .find the original no.

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Answer 1

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to both of them the fraction becomes 2/3.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The original number.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the numerator be r

Let the denominator be m

$\boxed{\bf{The\:original\:number=\frac{r}{m} }}}}$

A/q

$\longrightarrow\sf{2r=m+2}\\\\\longrightarrow\sf{m=2r-2....................(1)}$

&

$\longrightarrow\sf{\dfrac{r+3}{m+3} =\dfrac{2}{3} }\\\\\longrightarrow\sf{3(r+3)=2(m+3)}\\\\\longrightarrow\sf{3r+9=2m+6}\\\\\longrightarrow\sf{3r-2m=6-9}\\\\\longrightarrow\sf{3r-2m=-3}\\\\\longrightarrow\sf{3r-2(2r-2)=-3\:\:\:[from(1)]}\\\\\longrightarrow\sf{3r-4r+4=-3}\\\\\longrightarrow\sf{-r=-3-4}\\\\\longrightarrow\sf{\cancel{-}r=\cancel{-}7}\\\\\longrightarrow\sf{\pink{r=7}}$

∴ Putting the value of r in equation (1),we get;

$\longrightarrow\sf{m=2(7)-2}\\\\\longrightarrow\sf{m=14-2}\\\\\longrightarrow\sf{\pink{m=12}}$

Thus;

$\boxed{\bf{The\:original\:number=\frac{r}{m} =\boxed{\bf{\frac{7}{12} }}}}}$

Answer 2

Solution:

◕Let the Numerator be = x

◕And denominator be = 2x -2

✷If 3 is added to both of them the fraction becomes 2/3

◍Then,

→Numerator = x+3

→Denominator = 2x-2+3 = 2x+1

✿ According to the ques,

➜Numerator/Denominator= 2/3

➜x+3/2x+1 = 2/3

➜3(x+3) = 2(2x+1)

➜3x+9 = 4x +2

➜3x-4x = 2-9

➜-x = -7

➜x = 7

☞Original numerator = x = 7

☞ Original denominator = 2x-2

→2(7) -2

→14-2

→12

Hence the Original fraction is = 7/12