Question

In a fraction twice the numerator is 2 more than the denominator if 3 is added to the numerator and tourism denominator the new fraction is 2 by 3 find the original fraction

Answer 1

Let numerator be x and denominator be y
Fraction is x/y
From 1st condition,
x=2+y....................(i)
From 2nd condition,
3+x/y=2/3
put x=2+y
3+(2+y)/y =2/3
[3y+(2+y)]/y = 2/3
[3y+2+3y+y]/y =2/3
[3y+2+3y+y] = 2y/3
3×[3y+2+3y+y] = 2y
9y +6 +9y+3y = 2y
21y-2y=-6
19y =-6
y=-6/19
put y=-6/19
x=2+6/19
x=(39+6)/19
x=45/19
Fraction = x/y
= (45/19)/(6/19)
= 45/19×19/6
= 45×6
=(45/1)×(6/1)
= (45/1)/(1/6)
= 45 /6

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