Question

The numerator of a fraction is 3 less than the denominator if 2 is added to the numerator and 4 is added to the denominator the resulting fraction becomes 2 x 3 find the fractions

Answer 1

Correct Question :

The numerator of a fraction is 3 less than the denominator. If 2 is added to the numerator and 4 is added to the denominator the resulting fraction becomes 2/3 . Find the fraction.

Given :

• The numerator of a fraction is 3 less than the denominator.
• If 2 is added to the numerator and 4 is added to the denominator the resulting fraction becomes 2/3 .

To find :

• The fraction.

Solution :

Let the numerator of the fraction be x and the denominator of the fraction be y.

According to the 1st condition :-

• The numerator of a fraction is 3 less than the denominator.

$\implies\sf{x=y-3..................eq(1)}$

According to the 2nd condition :-

• If 2 is added to the numerator and 4 is added to the denominator the resulting fraction becomes 2/3 .

$\implies\sf{\dfrac{x+2}{y+4}=\dfrac{2}{3}}$

Put x=y-3 from eq(1).

$\implies\sf{\dfrac{y-3+2}{y+4}=\dfrac{2}{3}}$

$\implies\sf{\dfrac{y-1}{y+4}=\dfrac{2}{3}}$

$\implies\sf{3y-3=2y+8}$

$\implies\sf{3y-2y=8+3}$

$\implies\sf{y=11}$

• Denominator = 11

Now put y = 11 in eq(1) for getting the value of x.

$\implies\sf{x=y-3}$

$\implies\sf{x=11-3}$

$\implies\sf{x=8}$

• Numerator = 8

Therefore,

${\boxed{\bold{Fraction=\dfrac{8}{11}}}}$

Answer 2

$\bold\blue{Correct \ Question}$

$\bold{The \ numerator \ of \ a \ fraction \ is}$

$\bold{3 \ less \ than \ the \ denominator.If \ 2}$

$\bold{is \ added \ to \ the \ numenator \ and \ 4}$

$\bold{is \ added \ to \ the \ denominator \ the}$

$\bold{resulting \ fraction \ become \ \frac{2}{3}.}$

$\bold{Find \ the \ fraction.}$

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\bold{Fraction \ is \ \frac{8}{11}.}$

$\orange{\underline{\underline{Given:}}}$

$\bold{=>The \ numerator \ of \ a \ fraction}$

$\bold{is \ 3 \ less \ than \ the \ denominator.}$

$\bold{=>If \ 2 \ is \ added \ to \ the \ numenator}$

$\bold{and \ four \ is \ added \ to \ the \ denominator}$

$\bold{resulting \ fraction \ becomes \ \frac{2}{3}.}$

$\bold\pink{To \ find:}$

$\bold{The \ fraction.}$

$\huge\green{\underline{\underline{Solution:}}}$

$\bold{Let \ the \ numerator \ be \ x \ and}$

$\bold{denominator \ be \ y.}$

$\bold{According \ to \ the \ first \ condition.}$

$\bold{x+3=y}$

$\bold{\therefore{x-y=-3...(1)}}$

$\bold{According \ to \ the \ second \ condition.}$

$\bold{\frac{x+2}{y+4}=\frac{2}{3}}$

$\bold{\therefore{3(x+2)=2(y+4)}}$

$\bold{\therefore{3x+6=2y+8}}$

$\bold{\therefore{3x-2y=8-6}}$

$\bold{\therefore{3x-2y=2...(2)}}$

$\bold{Multiply \ equation \ (1) \ by \ 2, \ we \ get}$

$\bold{2x-2y=-6...(3)}$

$\bold{Subtract \ equation \ (2) \ from \ equation \ (3),}$

$\bold{we \ get}$

$\bold{3x-2y=2}$

$\bold{-}$

$\bold{2x-2y=-6}$

$\bold{(-) \ (-) \ \ (+)}$

____________________

$\bold{\therefore{x=8}}$

$\bold{Substituting \ x=8 \ in \ equation \ (1),}$

$\bold{we \ get}$

$\bold{8-y=-3}$

$\bold{-y=-3-8}$

$\bold{-y=-11}$

$\bold{\therefore{y=11}}$

$\bold{Fraction=\frac{x}{y}=\frac{8}{11}}$

$\bold\purple{\tt{\therefore{Fraction \ is \ \frac{8}{11}.}}}$