Question

36. 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 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.

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