Question

The denominator of a rational number is greater than its Numerator by 6. If the Numerator is increased by 5 and Denominator is decreased by 3,the number obtained is 5/4.Find the rational number​

Answer 1

Step-by-step explanation:

x = 5 is right answer. for more details follow me

Answer 2

Answer:

What we have to find : -

• The rational number.

Solution :

Let us take the numerator as x

Now,the denominator will be x+6

It is also given that,numerator is increased

by 5 and denominator is decreased by 3.

Therefore,The numerator of new rational number= x+5

Denominator of new rational number

=(x+6)-3

=x+3

The new rational number=$\frac{x + 5}{x + 3}$

The given rational number=$\frac{5}{4}$

$\frac{x + 5}{x + 3} = \frac{5}{4}$

The next step will solved by Cross

Multiplication.

→ 4(x+5) = 5(x + 3)

→ 4x + 20 = 5x + 15

→ 4x-5x = 15 -20

→$- x = - 5$

→x=5

Therefore,

Numerator of rational number=5

Denominator of rational number=5+6=11

Hence,the rational number=$\frac{5}{11}$

Verification :

$\frac{Original Numerator + 5}{Original Numerator - 3}$

=$\frac{5 + 5}{11 - 3}$

=$\frac{10}{8}$

=$\frac{5}{4}$

Thus, the solution is Verified.