Question

24. If 2 is added to the numerator of a fraction, it reduces to 1/2
and if 1 is
subtracted from the denominator, it reduces to 1/3.
Find the fraction​
solve step by step

Answer 1

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

If 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from the denominator, it reduces to 1/3.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The fraction.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the numerator be r

Let the denominator be m

$\bf{\boxed{\bf{The\:fraction=\frac{r}{m} }}}}}$

A/q

$\underbrace{\bf{1_{st}\:Case\::}}}}}$

$\longrightarrow\sf{\dfrac{r+2}{m} =\dfrac{1}{2} }\\\\\\\longrightarrow\sf{2(r+2)=m}\\\\\\\longrightarrow\sf{2r+4=m....................(1)}$

$\underbrace{\bf{2_{nd}\:Case\::}}}}}$

$\longrightarrow\sf{\dfrac{r}{m-1} =\dfrac{1}{3}} \\\\\\\longrightarrow\sf{3r=1(m-1)}\\\\\\\longrightarrow\sf{3r=m-1}\\\\\\\longrightarrow\sf{3r=2r+4-1\:\:\:\:[from(1)]}\\\\\\\longrightarrow\sf{3r=2r+3}\\\\\\\longrightarrow\sf{3r-2r=3}\\\\\\\longrightarrow\sf{\pink{r=3}}$

Putting the value of r in equation (1),we get;

$\longrightarrow\sf{m=2(3)+4}\\\\\longrightarrow\sf{m=6+4}\\\\\longrightarrow\sf{\pink{m=10}}$

Thus;

$\bf{\boxed{\bf{The\:fraction=\frac{r}{m}=\frac{3}{10} }}}}}$

Answer 2

$\huge\bf{\underline{\pink{Question:-}}}$

24. If 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from the denominator, it reduces to 1/3. Find the fraction.

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$\large\bf{\underline{\purple{Answer:-}}}$

Fraction is 3/10.

$\large\bf{\underline{\orange{ExPlanATiOn:-}}}$

$\large\bf{\underline{\green{Given:-}}}$

It is given that if we add 2 to the numerator of fraction it reduces 1/2.

and if 1 is substracted from the denominator it reduces 1/3.

$\large\bf{\underline{\green{To\:Find:-}}}$

we need to find the fraction.

$\huge\bf{\underline{\red{Solution:-}}}$

Let the fraction be x.

According to 1st condition

if we add 2 to the numerator it reduces 1/2

$\bf\frac{x+2}{y}=\frac{1}{2}$

$\bf:\implies\:(x+2)2=y$

$\bf:\implies\:y=2x+4............1$

According to 2nd condition

If we substract 1 from the fraction it reduces 1/3.

$\bf:\implies\:\frac{x}{y-1}=\frac{1}{3}$

$\bf:\implies\:3x = y-1$

$\bf:\implies\:x=\frac{y-1}{3}.............2$

Now solving equations.

Substituting value of y from 1st equation in equation 2 .

$\bf:\implies\:x=\frac{(2x+4)-1}{3}$

$\bf:\implies\:3x=2x+3$

$\bf:\implies\:3x-2x=3$

$\bf:\implies\:{\underline{\boxed{x=3}}}$

Putting value of x in equation 1.

$\bf:\implies\:y= 2\times3+4$

$\bf:\implies\:y=6+4$

$\bf:\implies\:{\underline{\boxed{y=10}}}$

$\bf:\implies\: Fraction=\frac{3}{10}$

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