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.

Answer 1

=x+2+3/x+3=2/3
=x+5/x+3 =2/3
=(x+5)3 =(x+3)2
=3x+15 =2x+6
=3x-2x =6-15
= x =-9
Original fraction =-9+2/-9
=-7/-9
=7/9

Answer 2

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

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