Question

7. The numerator of a fraction is 4 less than the denominator. If the
numerator is decreased by 2 and the denominator is increased by 1, then
the denominator is 8 times the numerator. Find the fraction.​

Answer 1

Answer:

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Answer 2

Solution :

$\bigstar$Let the numerator of fraction be r & denominator of fraction be m

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

A/q

$\longrightarrow\sf{r=m-4................(1)}$

&

$\longrightarrow\sf{8(r-2)=m+1}\\\\\longrightarrow\sf{8r-16=m+1}\\\\\longrightarrow\sf{8r-m=1+16}\\\\\longrightarrow\sf{8r-m=17}\\\\\longrightarrow\sf{8(m-4)-m=17\:\:\:[from(1)]}\\\\\longrightarrow\sf{8m-32-m=17}\\\\\longrightarrow\sf{8m-m=17+32}\\\\\longrightarrow\sf{7m=49}\\\\\longrightarrow\sf{m=\cancel{49/7}}\\\\\longrightarrow\bf{m=7}$

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

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

Thus;

$\boxed{\sf{Numerator\:of\:fraction=r=3}}}\\\boxed{\sf{Denominator\:of\:fraction=m=7}}}$

$\boxed{\sf{The\:fraction\:become\:=\frac{r}{m} =\boxed{\bf{\frac{3}{7} }}}}}$