Question

Q8. Denominator of a fraction is 4 less than its numerator. If 3 is subtracted from the numerator and denominator, the fraction obtained is 9/7 . Find the fraction​

Answer 1

Question:-

• Denominator of a fraction is 4 less than its numerator. If 3 is subtracted from the numerator and denominator, the fraction obtained is 9/7 . Find the fraction.

To Find:-

• Find the fraction.

Solution:-

• Let the numerator be ' x '

• Denominator be ' x - 4 '

According to the Question:-

$\longrightarrow\sf \: \dfrac { x - 3 } { x - 4 - 3 } = \dfrac { 9 } { 7 }$

$\longrightarrow\sf \: \dfrac { x - 3 } { x - 7 } = \dfrac { 9 } { 7 }$

$\longrightarrow\sf \: 7( x - 3 ) = 9( x - 7 )$

$\longrightarrow\sf \: 7x - 21 = 9x - 63$

$\longrightarrow\sf \: 9x - 7x = 63 - 21$

$\longrightarrow\sf \: 2x = 42$

$\longrightarrow\sf \: x = \cancel\dfrac { 42 } { 2 }$

$\longrightarrow\sf \: x = 21$

Hence ,

• Numerator is 21

• Denominator is x - 4 = 17

Answer 2

${ \large{ \underline{ \sf{ \pmb{Given...}}}}}$

• Denominator of a fraction is 4 less than its numerator.

• If 3 is subtracted from the numerator and denominator, the fraction obtained is 9/7

${ \large{ \underline{ \sf{ \pmb{To \: Find ...}}}}}$

• The original fraction respectively

${ \large{ \underline{ \sf{ \pmb{Solution ...}}}}}$

➱ Now,

• Let's consider the numerator of the original fraction as x + 4

➱ And,

• Let the denominator of the original fraction be assumed as x

↝So, the original fraction will be,

$\longrightarrow \tt \: \dfrac{x + 4}{x}$

➼Now,

• According to the condition we get,

${ : \implies} \rm \frac{x + 4 - 3}{x - 3} = \frac{9}{7} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \frac{x + 1}{x - 3} = \frac{9}{7} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: 7(x + 1) = 9(x - 3) \\ \\ \\ { : \implies} \rm 7x + 7 = 9x - 27 \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm 7 = 9x - 27 - 7x \: \: \: \: \: \\ \\ \\ { : \implies} \rm 7 = 9x - 7x - 27 \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm 7 = 2x - 27 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm 2x = 7 + 27 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\{ : \implies} \rm 2x = 34 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: x = \cancel \frac{34}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies}{ \pink{ \underline{ \boxed{ \frak{x =17}}} \bigstar}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Now let's find the fraction

$\longmapsto \tt \: \frac{x + 4}{x} = \frac{17 + 4}{17} \\ \\ \\ \longmapsto \tt \: \frac{21}{17} \star \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth the fraction is 21/17

${ \large{ \underline{ \sf{ \pmb{Verification...}}}}}$

• Let's apply the second condition to check weather we went right

${ : \implies} \rm \frac{21 - 3}{17 - 3} = \frac{9}{7} \\ \\ \\ { : \implies} \rm \frac{18}{14} = \frac{9}{7} \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: \frac{9}{7} = \frac{9}{7} \: \: \: \: \: \: \:$

• Hence Verified...!!!