Question

The denominator 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. Don't spam otherwise you will be reported​

Answer 1

Answer:

Suppose numerator of the rational number is p, then denominator is p+8.

Rational number is  

p+8

p

​

.

Numerator is increased by 17, then it becomes p+17.

Denominator is decreased by 1, then it becomes p+8−1=p+7

New rational number is  

p+7

p+17

​

=  

2

3

​

 

⇒2p+34=3p+21

⇒p=13

Thus numerator is 13.

Denominator is p+8=13+8=21

Therefore, the rational number is  

21

13

​

.

Step-by-step explanation:

Answer 2

$\sf\huge\bold{Answer:}$

Given :

Denominator = Numerator +5 i.e. d=n+5

(n+6)/(d-4) = 3/2

To find :

The rational number

Solution :

Let numerator be n

& Denominator be d

According to question

$\tt\ rational \: no. = \frac{numerator}{denominator}$

$\tt\ no. = \frac{n}{d}$

Original Condition

$\tt\ no. = \frac{n}{n + 5} ...(1)$

New condition

$\tt\ \frac{n + 6}{(n + 5) - 4} = \frac{3}{2}$

$\tt\ \frac{2(n + 6)}{n + 5 - 4} = \frac{3}{1}$

$\tt\ \frac{2n + 12}{n + 1} = \frac{3}{1}$

$\tt\ 2n + 12 = 3(n + 1)$

$\tt\ 2n + 12 = 3n + 3$

$\tt\ 12 - 3 = 3n - 2n$

$\tt\ 9 =n$

$\tt\ n = 9$

$\tt\ d = n + 5 = 9 + 5 = 14$

$\boxed{\red{ \tt\ rational \: number = \frac{n}{d} = \frac{9}{14} }}$