Question

by
16). In a fraction, twice the numerator is 2 more than
the denominator. If 3 is added to the numerator

and to the denominator, the new fraction is 2/3
Find the original fraction.​

Answer 1

Answer:

$\large\bold\red{\frac{7}{12}}$

Step-by-step explanation:

Let the required fraction be $\large{\frac{x}{y}}$

Where,

• Numerator = x
• Denominator = y

Now,

According to question,

Twice the Numerator is 2 more than Denominator.

Therefore,

We get,

$= > 2x = y + 2 \\ \\ = > y = 2x - 2\: \: \: \: .........(1)$

Also,

If 3 is added to the Numerator and to the Denominator , the fraction becomes 2/3.

Therefore,

We get,

$= > \frac{x + 3}{y + 3} = \frac{2}{3}$

Substituting the value of y from (1),

We get,

$= > \frac{x + 3}{2x - 2 + 3} = \frac{2}{3} \\ \\ = > 3( x + 3) = 2(2x + 1) \\ \\ = > 3x + 9 = 4x + 2 \\ \\ = > 4x - 3x = 9 - 2 \\ \\ = > x = 7$

Therefore,

We get,

$= > y = 2 \times 7 - 2 \\ \\ = > y = 14- 2 \\ \\ = > y = 12$

Hence,

The required fraction is $\large\bold{\frac{7}{12}}$

Answer 2

Correct Question :

In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to the numerator and to the denominator, the new fraction is 2/3 . Find the original fraction.

Given :

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

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

To find :

The original fraction.

Solution :

Let the numerator be x and the denominator be y .

According to the 1st condition :-

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

$\implies\sf{2x=y+2}$

$\implies\sf{y=2x-2........eq(1)}$

According to 2nd condition :-

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

$\implies\sf{\frac{x+3}{y+3}=\frac{2}{3}}$

$\implies\sf{3x+9=2y+6}$

✪ Now put the value of y=2x-2 from eq (1)✪

$\implies\sf{3x+9=2(2x-2)+6}$

$\implies\sf{3x+9=4x-4+6}$

$\implies\sf{3x-4x=-9+2}$

$\implies\sf{-x=-7}$

$\implies\sf{x=7}$

✪ Now put x = 7 in eq(1) ✪

$\implies\sf{y=2x-2}$

$\implies\sf{y=2\times\:7-2}$

$\implies\sf{y=14-2}$

$\implies\sf{y=12}$

★ Numerator = 7

★ Denominator = 12

${\boxed{\bold{Fraction=\dfrac{Numerator}{Denominator}}}}$

Therefore,

${\boxed{\purple{\bold{Original\: fraction=\dfrac{x}{y}=\dfrac{7}{12}}}}}</p><p>$