Question

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

Answer 1

Answer:

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

Answer 2

$\\ \large{\sf{\pmb{\underline{\underline{Question:}}}}}$

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

$\\ \large{\sf{\pmb{\underline{\underline{Required \: Answer:}}}}}$

$\\ \sf{\tt{\underline{\underline{Given:}}}}$

• Denominator of the fraction is greater than the numerator by 8.
• If the numerator is increased by 17 and denominator is decreased by 1, the number obtained is 3/2.

$\\ \sf{\tt{\underline{\underline{To \: Find:}}}}$

• The fraction.

$\\ \sf{\tt{\underline{\underline{Solution:}}}}$

Let us assume that,

• The numerator of the fraction is x
• Hence, the denominator of the fraction is x+8

∴ The rational number will be x/x+8

According to the given condition,

• New numerator = x+17
• New denominator = x+8-1

According to the question:-

$\\ \bold{ \dfrac{x + 17}{x + 8 - 1} = \dfrac{3}{2}}$

$\\ \sf{\implies{ \dfrac{x + 17}{x + 7} = \dfrac{3}{2}}}$

$\\ \sf{\implies{ 3(x + 7) = 2(x + 17)}}$

$\\ \sf{\implies{3x + 21 = 2x + 34}}$

$\\ \sf{\implies{3x - 2x = 34 - 21}}$

$\\ \sf{\therefore{x = \bold{13}}}$

$\\ \sf{\therefore{The \: fraction = \dfrac{x}{x + 8} = \dfrac{13}{13 + 8} = \bold{\red{\dfrac{13}{21}}}} }$

$\\ \underline{\rm{Hence, \: the \: fraction \: is \: \green{ \dfrac{13}{21}}}}$