Question

The denominator of a rational number is less thanless than its numerator by 55. If the numerator is decreased bydecreased by 2020 and the denominator is increased byincreased by 2424, the new rational number becomes 710710. Find the original rational number.​

Answer 1

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

hope it helpful to you....

Answer 2

Answer:

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