Question

denominator of a rational number is 4 less than its numerator. if 11 is added to numerator & 1 is subtracted from denominator then the new number becomes 7/3 find the rational number.​

Answer 1

Answer

Let the numerator be x.

Let the denominator be x - 4.

So, the fraction becomes

$\sf \dashrightarrow \dfrac{x}{x - 4}$

We are also given that 11 is added to the numerator and 1 is subtracted from the denominator. So, the fraction becomes

$\sf \dashrightarrow \dfrac{x + 11}{(x - 4) - 1}$

We are also given with the fraction which is obtained when the numerator is dectlreased and numerator is increased. The fraction is

$\sf \dashrightarrow \dfrac{7}{3}$

Numerator of the fraction :

According to the question,

$\sf \dashrightarrow \dfrac{x + 11}{(x - 4) - 1} = \dfrac{7}{3}$

$\sf \dashrightarrow 3(x + 11) = 7(x - 4 - 1)$

$\sf \dashrightarrow 3(x + 11) = 7(x - 5)$

$\sf \dashrightarrow 3x + 33 = 7x - 35$

$\sf \dashrightarrow 3x - 7x = -35 - 33$

$\sf \dashrightarrow -4x = -68$

$\sf \dashrightarrow x = \dfrac{-68}{-4}$

$\sf \dashrightarrow x = 17$

Now, we can find the denominator of the fraction.

Denominator of the fraction :

$\sf \dashrightarrow x - 4$

$\sf \dashrightarrow 17 - 4$

$\sf \dashrightarrow 13$

So, the fraction becomes

$\sf \dashrightarrow \dfrac{17}{13}$

Hence, the original fraction is 17/13.

Answer 2

Let the numerator be x.

Let the denominator be x - 4.

So, the fraction becomes

x}{x - 4}⇢

x−4

x

We are also given that 11 is added to the numerator and 1 is subtracted from the denominator. So, the fraction becomes

{x + 11}{(x - 4) - 1}⇢

(x−4)−1

x+11

We are also given with the fraction which is obtained when the numerator is dectlreased and numerator is increased. The fraction is

{7}{3}⇢

3

7

Numerator of the fraction :

According to the question,

{x + 11}{(x - 4) - 1} = {7}{3}⇢

(x−4)−1

x+11

=

3

7

3(x + 11) = 7(x - 4 - 1)⇢3(x+11)=7(x−4−1)

3(x + 11) = 7(x - 5)⇢3(x+11)=7(x−5)

3x + 33 = 7x - 35⇢3x+33=7x−35

3x - 7x = -35 - 33⇢3x−7x=−35−33

-4x = -68⇢−4x=−68

x = {-68}{-4}⇢x=

−4

−68

x = 17⇢x=17

Now, we can find the denominator of the fraction.

Denominator of the fraction :

x - 4⇢x−4

17 - 4⇢17−4

13⇢13

So, the fraction becomes

{17}{13}⇢

13

17

Hence, the original fraction is 17/13.

Unlucky man in the world!