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

Age of a rational number???

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

​

.