Math, asked by 07miracle, 11 months ago

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

Answers

Answered by sanishaji30
1

let the numerator be x

denominator = 2x-2

3 is added :-

Numerator= x+3

Denominator= 2x-2+3

=2x+1

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

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

3x+9=4x+2

3x-4x=2-9

-x=-7

x=7

Original Numerator = x = 7

Original Denominator = 2x-2

= 2(7)-2

= 14-2

= 12

Original Fraction = 7/12

Answered by AnIntrovert
0

\bold\red{\underline{\underline{Answer:}}}

Fraction is \bold{\frac{7}{12}}

\bold\green{\underline{\underline{Solution}}}

Let the numerator be x and denominator be y.

According to the first condition

2x=y+2

2x-y=2...(1)

According to the second condition

\bold{\frac{x+3}{y+3}=\frac{2}{3}}

\bold{3(x+3)=2(y+3)}

\bold{3x+9=2y+6}

\bold{3x-2y=-3...(2)}

Multiply equation (1) by 2

4x-2y=4...(3)

Subtract equation (2) from equation (3), we get

4x-2y=4

-

3x-2y=-3

x=7

Substituting x=7 in equation (1), we get

2(7)-y=2

14-y=2

-y=4-14

-2y=-12

\bold{y=\frac{-12}{-1}}

y=12

Fraction is \bold{\frac{x}{y}}

i.e \bold{\frac{7}{12}}

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