The sum of numerator and denominator of a fraction is 3 less than twic

1.	The sum of numerator and denominator of a fraction is 3 less than twice the denominator. If each of the numerator and denominator is decreased by 1, the fraction becomes 12. Find the fraction
Answer» SOLUTION : $\underline{\bf{Given\::}}}}$ The sum of numerator & denominator of a fraction is 3 LESS than twice the denominator. If each of the numerator & denominator is DECREASED by 1, the fraction becomes 1/2. $\underline{\bf{Explanation\::}}}}$ Let the numerator digit be r & denominator digit be m $\boxed{\bf{The\:fraction\:becomes=\frac{r}{m} }}}$ A/q $\longrightarrow\sf{r+m+3=2m}\\\\\longrightarrow\sf{r+m-2m=-3}\\\\\longrightarrow\sf{r-m=-3}\\\\\longrightarrow\bf{r=-3+m......................(1)}$ & $\longrightarrow\sf{\dfrac{r-1}{m-1} =\dfrac{1}{2} }\\\\\longrightarrow\sf{2(r-1)=1(m-1)}\\\\\longrightarrow\sf{2r-2=m-1}\\\\\longrightarrow\sf{2(-3+m)-2=m-1\:\:[from(1)]}\\\\\longrightarrow\sf{-6+2m-2=m-1}\\\\\longrightarrow\sf{-8+2m=m-1}\\\\\longrightarrow\sf{2m-m=-1+8}\\\\\longrightarrow\bf{m=7}$ ∴ Putting the value of m in equation (1),we get; $\longrightarrow\sf{r=-3+7}\\\\\longrightarrow\bf{r=4}$ Thus; $\boxed{\sf{The\:fraction\:becomes=\frac{r}{m}=\boxed{\bf{\frac{4}{7} }}}}$

The sum of numerator and denominator of a fraction is 3 less than twice the denominator. If each of the numerator and denominator is decreased by 1, the fraction becomes 12. Find the fraction

Answer»

SOLUTION :

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

The sum of numerator & denominator of a fraction is 3 LESS than twice the denominator. If each of the numerator & denominator is DECREASED by 1, the fraction becomes 1/2.

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

Let the numerator digit be r & denominator digit be m

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

A/q

$\longrightarrow\sf{r+m+3=2m}\\\\\longrightarrow\sf{r+m-2m=-3}\\\\\longrightarrow\sf{r-m=-3}\\\\\longrightarrow\bf{r=-3+m......................(1)}$

&

$\longrightarrow\sf{\dfrac{r-1}{m-1} =\dfrac{1}{2} }\\\\\longrightarrow\sf{2(r-1)=1(m-1)}\\\\\longrightarrow\sf{2r-2=m-1}\\\\\longrightarrow\sf{2(-3+m)-2=m-1\:\:[from(1)]}\\\\\longrightarrow\sf{-6+2m-2=m-1}\\\\\longrightarrow\sf{-8+2m=m-1}\\\\\longrightarrow\sf{2m-m=-1+8}\\\\\longrightarrow\bf{m=7}$

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

$\longrightarrow\sf{r=-3+7}\\\\\longrightarrow\bf{r=4}$

Thus;

$\boxed{\sf{The\:fraction\:becomes=\frac{r}{m}=\boxed{\bf{\frac{4}{7} }}}}$

The sum of numerator and denominator of a fraction is 3 less than twice the denominator. If each of the numerator and denominator is decreased by 1, the fraction becomes 12. Find the fraction

SOLUTION :

&

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