Question

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

Answer 1

The fraction is 13/21

Answer 2

Solution:-

$\sf \bold{\: Let}$

$\begin{gathered} : \mapsto \bf\:N umerator \: be \: x \\ : \mapsto \bf \: Denominator = x + 8\end{gathered}$

♠ As we know that -

$\bf \mapsto \: \pink{ \boxed{ \sf \bigstar Fraction = \frac{Numerator}{Denominator}}}$

Now, Adding 17 with Numerator and decreasing 1 from denominator.

$\begin{gathered} \rm \longrightarrow \maltese \: \purple{New \: numerator = x + 17 }\\ \\ \longrightarrow \rm \maltese \purple{ \:New \: denominator = {x + 8 - 1 } }\\ \leadsto \rm \purple{x + 7}\end{gathered}$

$\leadsto \clubs \: \bf N ew \: fraction = \frac{3}{2}$

ACQ,

$\begin{gathered} \therefore \tt \frac{x +17 }{x + 7} = \frac{3}{2} \\ \\ \tt \dashrightarrow3(x + 7) = 2( x + 17) \\ \\ \tt \dashrightarrow3x + 21 = 2x + 34 \\ \\ \tt \dashrightarrow3x - 2x = 34 - 21 \\ \\ \tt \dashrightarrow \: \fcolorbox{purple}{green}{x = 13}\end{gathered}$

$\begin{gathered} \leadsto \bigstar \bf \: Numerator = x = \color{aqua}13 \\ \\ \bf \leadsto \bigstar \: Denominator = x + 8 \\ \\ \twoheadrightarrow \: \bf13 + 8 \ \\ \\ \ \twoheadrightarrow \: \bf\pink{ 21} \\ \\ \\ \looparrowright \green{ \underbrace{ \bf\:Fraction = \frac{13}{21} }}\end{gathered}$