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

let the numerator of the fraction be x and denominator be y
original fraction=x/y
2x=y+2
2x-y=2.....(eqn 1)
3+x/3+y=2/3
(3+x)3=(3+y)2
9+3x=6+2y
3x-2y=6-9
3x-2y=-3......(eqn 2)
(eqn 1)*2
(2x-y=2)*2
4x-2y=4.....(eqn 3)
subtracting eqn 2 from eqn 3
4x-2y-4-(3x-2y+3)=0
4x-2y-4-3x+2y-3=0
x-7=0
x=7
substituting x=7 in eqn 1
2x-y=2
14-y=2
14-2=y
16=y
original fraction=x/y
7/16

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