Question

in a fraction twice the numerator is 2 more than the denominator if 3 is added to the numerator and the denominator the new fraction is 2 upon 3 find the original fraction​

Answer 1

Let the numerator be N and denominator be D.

In a fraction twice the numerator is 2 more than the denominator.

According to question,

=> $\sf{2N \:=\: D\: +\: 2}$

=> $\sf{2N\: - \:2 \:=\: D}$ ___ (eq 1)

If 3 is added to the numerator and the denominator the new fraction is 2/3.

According to question,

=> $\sf{\frac{N\:+\:3}{D\:+\:3}\:=\:\frac{2}{3}}$

=> $\sf{3(N\:+\:3)\:=\:2(D\:+\:3)}$

=> $\sf{3N\:+\:9\:=\:2D\:+\:6}$

=> $\sf{3N\:+\:9\:-\:6\:=\:2(2N\:-\:2)}$

[From (eq 1)]

=> $\sf{3N\:+\:3\:=\:4N\:-\:4}$

=> $\sf{3N\:-\:4N\:=\:-\:4\:-\:3}$

=> $\sf{-N\:=\:-7}$

=> $\sf{N\:=\:7}$

Substitute value of N in (eq 1)

=> $\sf{2(7)\:-\:2\:=\:D}$

=> $\sf{14\:-\:2\:=\:D}$

=> $\sf{D\:=\:12}$

•°• Fraction = Numerator/Denominator = 7/12.

Answer 2

Answer:

7/12

Step-by-step explanation:

Let the numerator be x.

It is given that numerator is 2 less than the twice of the denominator.

fraction- x/2x - 2

When we add 3 to the numerator and the denominator, the fraction becomes 2/3.

From this we got an equation :

x + 3/ 2x + 1 = 2/3

Solution :-

⇒ x + 3/ 2x + 1 = 2/3

⇒ (x + 3)3 = (2x + 1)2

⇒ 9-2 = 4x - 3x

⇒ 7 = x

So, we got numerator as 7

denominator : 2x - 2 = 12

Fraction : 7/12