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

Answer:

7/12

Step-by-step explanation:

Let the numerator be x

denominator will = 2x−2

If 3 is added to both then fraction =

3/2

ATQ ⇒(x+3)/(2x-2+3)=2/3

       ⇒ (x+3)/(2x+1)=2/3

       ⇒ 3(x+3)=2(2x+1)

       ⇒3x+9=4x−4+6

       ⇒7=x

∴ Denominator =2x−2=12

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