The denominator of a rational number is greater than the numerator by 6. If the numerator is deceased by 4, the new rational number become 1/5 . Find the original number.
Answers
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+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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Answer:
The denominator of a rational number is greater than the numerator by 6. If the numerator is deceased by 4, the new rational number become 1/5 . Find the original number..
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