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

Heya,

Let the numerator be x
So, the dinominator be y

y + 2 = 2x
=> y = 2x - 2

So, the fraction = x/2x - 2

According to Question,

$\frac{x + 3}{2x - 2 + 3} = \frac{2}{3}$

=> 3(x + 3) = 2(2x +1)
=> 3x + 9 = 4x + 2
=> 9 - 2 = 4x - 3x
=> 7 = x

∴ Numerator = x = 7
Dinominator = 2x - 2
= 2(7) - 2
= 14 - 2
= 12

∵ Required faction is 7/12

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