English, asked by shardulsawant666, 1 month ago

a. The denominator of a rational number is greater than its numerator by 5. If the numerator is
increased by 11 and the denominator is decreased by 14, the new number becomes 5. Find the
original rational number.

Answers

Answered by amitsharma777222999
2

Explanation:

numerator=x

denominator=x+5

x+11/x+5-14 =5

x+11/x-9=5

x+11=5x-45

4x=56

x=14

x+5=19

original number=14/19

Answered by SachinGupta01
19

 \sf \implies  Let  \: the \:  numerator \:  of  \: the \:  fraction \:  be \:  x

 \sf Then  \: according \:  to  \: question,

 \sf \implies  The  \: denominator \:  will \:  be \:  (x+5)

 \sf  \underline{Conditions \:  given \:  in \:  the  \: question  \: are} :

If the Numerator is increased by 11 and the Denominator is decreased by 14, then the number becomes 5.

 \sf  \underline{Hence, our \:  equation  \: will \:  be} :

 \red{\implies\bf \dfrac{(x + 11)}{(x + 5 - 14)} = 5}

 \sf  \underline{Now, we \:  will \:  solve  \: the  \: above \:  equation. }

\implies\sf \dfrac{(x + 11)}{(x  - 9)} = 5

\implies\sf x + 11 = 5x - 45

\implies\sf  - 4x  + 11 =  - 45

\implies\sf  - 4x   =   - 45 - 11

\implies\sf  - 4x   =    - 56

\implies\sf  x   =  \dfrac{ - 56}{ - 4}

\implies\sf  x   =  14

 \sf \underline{Therefore},

\implies\sf  Numerator  \: (x) = 14

\sf\implies  Denominator \:  (x+5) = 14+5 = 19

 \underline{ \boxed{ \sf \pink{Thus, the  \: original \:  fraction \:  is   \: \dfrac{14}{19} } }}

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