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.




if you will solve I will mark you as brainliest​

Answer 1

Given :

• In a fraction, twice the numerator is 2 more than the denominator.
• When 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 of the fraction be x.

Let the denominator of the fraction be y.

Fraction → $\mathtt{\red{\dfrac{x}{y}}}$

Case 1 :

$\mathtt{2(Numerator)\:=\:Denominator\:+\:2}$

➤ $\mathtt{2x=y+2}$

$\mathtt{2x-y=2}$ ____(1)

Case 2:

★ Provided, 3 is added to the numerator and denominator.

•°• Numerator → x + 3

Denominator → y + 3

•°• New fraction → 2/3

Equation :

➤ $\mathtt{\dfrac{(x+3)}{(y+3)}\:=\:{\dfrac{2}{3}}}$

➤ $\mathtt{3(x+3)=2(y+3)}$

➤ $\mathtt{3x+9=2y+6}$

➤ $\mathtt{3x-2y=6-9}$

$\mathtt{3x-2y=-3}$ ____(2)

★ Multiply equation (1) by 2,

➤ $\mathtt{2\:\times\:2x\:-2\:\times\:y\:=\:2\:\times\:2}$

$\mathtt{4x-2y=4}$ ____(3)

★ Solve equation (2) and (3) to find value of x and y.

★ Subtract equation 3 from 2,

➤ $\mathtt{3x-2y-(4x-2y)=-3-(4)}$

➤ $\mathtt{3x-2y-4x+2y=-3-4}$

➤ $\mathtt{3x-4x=-7}$

➤ $\mathtt{-x=-7}$

➤ $\mathtt{x=7}$

★ Substitute, x = 7 in equation 1,

➤ $\mathtt{2x-y=2}$

➤ $\mathtt{2(7)-y=2}$

➤ $\mathtt{14=2+y}$

➤ $\mathtt{14-2=y}$

➤ $\mathtt{12=y}$

$\large{\boxed{\sf{\red{Numerator\:=\:x\:=\:7}}}}$

$\large{\boxed{\sf{\purple{Denominator \:=\:y\:=\:7</p><p>12}}}}$

$\large{\boxed{\sf{\pink{Fraction\:=\:{\dfrac{x}{y}\:=\dfrac{7}{12}}}}}}$

Answer 2

$\huge\mathfrak\green{Answer:-}$

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 $\sf\dfrac{2}{3}$

Find:

We need to find the original fraction.

Solution:

Let the numerator be x

Denominator = 2x-2

when 3 is added :-

Numerator= x+3

Denominator= 2x-2+3 =2x+1

Now,

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

3(x+3)=2(2x+1)

3x+9=4x+2

3x-4x=2-9

-x=-7[cancelling the negative sign on both sides]

=> x=7

Original Numerator = x = 7

Original Denominator = 2x-2

Putting the value of x=7, we get,

= 2(7)-2

= 14-2

= 12

Hence, The Original Fraction is$\bf\dfrac{7}{12}$