Question

the denominator of a fraction is four more than the numerator. if the numerator and the denominator are both decreased by 1, the fraction becomes 5/7. find the fraction​

Answer 1

S O L U T I O N :

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

The denominator of a fraction is four more than the numerator. If the numerator & the denominator are both decreased by 1, the fraction becomes 5/7 .

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

Let the numerator place be r & the denominator place be (r+4) respectively.

$\boxed{\bf{The\:fraction=\frac{r}{r+4} }}$

$\underline{\underline{\tt{According\:to\:the\:question\::}}}$

$\mapsto\tt{\dfrac{r-1}{r+4-1} =\dfrac{5}{7} }$

$\mapsto\tt{\dfrac{r-1}{r+3} =\dfrac{5}{7} }$

$\mapsto\tt{7(r-1)=5(r+3)\:\:\:\underbrace{\sf{cross-multiplication}}}$

$\mapsto\tt{7r - 7 = 5r + 15}$

$\mapsto\tt{7r - 5r = 15+7}$

$\mapsto\tt{2r = 22}$

$\mapsto\tt{r= \cancel{22/2}}$

$\mapsto\bf{r=11}$

Now;

• Numerator = r = 11
• Denominator = (r+4) = (11+4) = 15

Thus;

$\boxed{\bf{The\:fraction=\frac{r}{r+4} =\frac{11}{11+4}=\frac{11}{15} }}$