Question

The denominator of a rational number is greater than its numerator by 6. If the numerator is increased by 19 and the denominator is decreased by 1, the number obtained is 5 3 . Find the rational number.​

Answer 1

Answer:

answer is below

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

.