Question

in a rational number the numerator is 2 more than the denominator if 3 is added to each the numerator and denominator the new fraction becomes 5.4 find the original number.....✨✨✨​

Answer 1

Question:

In a rational number the numerator is 2 more than the denominator. If 3 is added to each the numerator and denominator the new fraction becomes 5/4. Find the rational number?

Solution:

Let number be M.

Fraction = $\dfrac{Numerator\:(N)}{Denominator\:(D)}$

» Numerator is 2 more than the denominator.

Now.. new Numerator = M and new Denominator = M + 2

Original Fraction = $\dfrac{M}{M\:+\:2}$

» If 3 is added to each the numerator and denominator the new fraction becomes 5/4.

• A.T.Q.

=> $\dfrac{M\:+\:3}{M\:+\:2\:+\:3}\:=\:\dfrac{5}{4}$

=> $\dfrac{M\:+\:3}{M\:+\:5}\:=\:\dfrac{5}{4}$

Cross-multiply them

=> 4(M + 3) = 5(M + 5)

=> 4M + 12 = 5M + 25

=> 4M - 5M = 25 - 12

=> - M = 13

=> M = - 13

_____________________________

Original Fraction = $\dfrac{-13}{-13\:+\:2}$

=> $\dfrac{-13}{11}$

___________ [ ANSWER ]

_____________________________

✡ From above calculations we get M = - 13

Put value of M in this equation :

→ $\dfrac{M\:+\:3}{M\:+\:5}\:=\:\dfrac{5}{4}$

→ $\dfrac{-13\:+\:3}{-13\:+\:5}\:=\:\dfrac{5}{4}$

→ $\dfrac{-10}{-8}\:=\:\dfrac{5}{4}$

→ $\dfrac{5}{4}\:=\:\dfrac{5}{4}$

_____ [ HENCE VERIFIED ]

_____________________________

Answer 2

Fraction = x/x + 2

According to Question;

(x + 3)/(x + 5) = 5/4

Cross-multiply

4(x + 3) = 5(x + 5)

4x - 5x = 25 - 12

x = -13

So;

x + 2 = 11

Fraction = -13/11