Question

The denominator of a rational number is greater than its numerator by 8. If the
numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2 , Find the number

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Answer 1

S O L U T I O N :

Let the numerator be r

Let the denominator be r + 8

$\boxed{\bf{The\:number=\frac{r}{r+8} }}}}$

A/q

$\longrightarrow\tt{\dfrac{r+17}{r+8-1} =\dfrac{3}{2}} \\\\\\\longrightarrow\tt{\dfrac{r+17}{r+7} =\dfrac{3}{2} }\\\\\\\longrightarrow\tt{2(r+17)=3(r+7)\:\:\underbrace{\sf{Cross-multiplication}}}\\\\\\\longrightarrow\tt{2r+34=3r+21}\\\\\\\longrightarrow\tt{2r-3r=21-34}\\\\\\\longrightarrow\tt{\cancel{-} r=\cancel{-}13}\\\\\\\longrightarrow\bf{r=13}$

$\bigstar$ Numerator = r = 13

$\bigstar$ Denominator = (r + 8) = (13 + 8) = 21

Thus;

$\boxed{\bf{The\:number=\frac{13}{13+8} =\boxed{\sf{\frac{13}{21} }}}}}$

Answer 2

Answer:

Step-by-step explanation:

let numerator be x  

∴the denominator will be x+8  

⇒x+17/x+8-1=3/2  

⇒x+17/x+7=3/2  

⇒2(x+17)=3(x+7)  

⇒2x+34=3x+21

⇒34-21=3x-2x    

⇒13=x  

∴x/x+8

=13/21