Question

When we add 6 to the numerator of a fraction, we get 1/2.whwn we add 7 to the denominator of the same fraction .we get 1/3.fing the fraction by forming two equations

Answer 1

⇝ Given :-

• When we add 6 to the numerator of a fraction, we get 1/2.

• When we add 7 to the denominator of the same fraction, we get 1/3.

⇝ To Find :-

• The Fraction by Forming 2 equations.

⇝ Solution :-

Let For the Original Fraction :

• Numerator = x

• Denominator = y

So Original Fraction is : $\dfrac{\text x}{\text y}$

❒ When 6 is added to The Numerator :

Fraction Becomes : $\dfrac{\text x+6}{\text y}$

★ According To Question :

$\dfrac{\text x + 6}{\text y} = \frac{1}{2}$

$:\longmapsto2(\text x + 6) = \text y$

$:\longmapsto2\text x + 12 = \text y$

$:\longmapsto2\bf x - y = - 12 \: ----(1)$

❒ When 7 is added to The Denominator :

Fraction Becomes : $\dfrac{\text x}{\text y+6}$

★ According To Question :

$\dfrac{\text x}{\text y + 7} = \frac{1}{3}$

$:\longmapsto3\text x = \text y + 7$

$:\longmapsto \bf 3x - y = 7 \: - - - - (2)$

✏ Subtracting (1) From (2) :

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf x = 19} }}}$

✏ Putting Value of x in (2) :

$:\longmapsto3 \times 19 - \text y = 7$

$:\longmapsto57 - \text y = 7$

$:\longmapsto - \text y = 7 - 57$

$:\longmapsto \cancel - \text y = \cancel- 50$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf y = 50} }}}$

As,

Original Fraction = $\dfrac{\text x}{\text y}$

Hence,

$\large\underline{\pink{\underline{\frak{\pmb{\text Original \:\: Fraction = \dfrac{19}{50} }}}}}$

Answer 2

Given :-

When we add 6 to the numerator of a fraction, we get 1/2.

and if we add 7 to the denominator of the same fraction, we get 1/3.

To Find :-

Fraction

Solution :-

Let

${\boxed{\frak{\pink{\underline{Fraction=\dfrac{N}{D}}}}}}$

◼ C A S E 1 :

$\sf\dfrac{N+6}{D}=\dfrac{1}{2}$

By cross multiplication

2(N + 6) = 1(D)

2N + 12 = D (i)

◼ C A S E 2

By cross multiplication

1(D + 7) =  3(N)

D + 7 = 3N

Using

2N + 12 + 7 = 3N

3N - 2N = 12 + 7

N = 19

Now, Using 1

2N + 12 = D

2(19) + 12 = D

38 + 12 = D

50 = D

Hence,

Fraction = N/D = 19/50