present age of a rational number is greater than its numerator by 5. if the numerator is increased by 6 and the denominator is decreased by

Question

present age of a rational number is greater than its numerator by 5. if the numerator is increased by 6 and the denominator is decreased by 4, the number obtained is 3/2. Find the rational number.​

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Madelyn 1 month 2021-08-16T10:37:01+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-16T10:38:44+00:00

    Answer:

    Age of a rational number???

    Can’t understand your question

    0
    2021-08-16T10:38:49+00:00

    Answer:

    Step-by-step explanation:

    Let the numerator of the rational number be x.  

    Then, the denominator of the rational number =x+6.

    It is given that the numerator is increased by 5 and the denominator is decreased by 3.

    ∴ the numerator of the new rational number =x+5.

    Denominator of the new rational number =(x+6)−3=x+3

    ∴ new rational number =  

    x+3

    x+5

    ​  

     

    But the new rational number is given as  

    4

    5

    ​  

    .

    ∴  

    x+3

    x+5

    ​  

    =  

    4

    5

    ​  

     

    By cross multiplying, we get,

    4(x+5)=5(x+3)

    ⇒4x+20=5x+15

    ⇒4x−5x=15−20    ….[Transposing 5x to LHS. and 20 to RHS]

    ⇒−x=−5 or x=5

    ∴ numerator of the rational number is 5 and denominator =  5+6 i.e. 11.

    ∴ the required rational number is  

    11

    5

    ​  

    .

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