Question

he denemonitor of rational number is greater than its numerator by 6. if numbeator is increased by 5 and denominator is decreased by 3 the number obtained of 5/4 . find the rational number.
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Answer 1

Answer:

Step-by-step explanation:

ANSWER

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+5/x+3

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But the new rational number is given as  

5/4

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.

∴  

x+5/x+3

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=  

5/4

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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  

5÷11

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