Question

In a fraction twice the numerator is 2 more than denominator .If 3 is added to the numerator and to the denominator the new fraction is 2/3 .find the original number​

Answer 1

Solution :

Let the numerator be x

Denominator = 2x − 2

Therefore the fraction = x/2x − 2

Given when 3 is added to both the numerator and denominator, the fraction becomes 2/3.

Hence (x + 3)/(2x − 2 + 3) = 2/3

⇒ (x + 3)/(2x + 1) = 2/3

⇒ 3x + 9 = 4x + 2

⇒ x = 7

Therefore the fraction 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 $\bold{\frac{7}{12}}$