Question

11. A, B and C together finish a work in 4 days. If A alone can finish the same
8 days and B in 12 days, find how long will C take to finish the work.​

Answer 1

$\sf\large\underline\purple{Given:-}$

$\sf{\implies Work\: finish\:_{(A+B+C)}=4\:days}$

$\sf{\implies Work\: finish\:_{(A)}=8\:days}$

$\sf{\implies Work\: finish\:_{(B)}=12\:days}$

$\sf\large\underline\purple{To\: Find:-}$

$\sf{\implies Work\: finish\:_{(C)}=?\:days}$

$\sf\large\underline\purple{Solution:-}$

• To calculate the work done by C alone at first we have to assume work done by C alone be x then putting the value which given in the question:-]

$\sf{\implies Let,\:\:A's\:one\:day\: work=\dfrac{1}{8}}$

$\sf{\implies Let,\:\:B's\:one\:day\: work=\dfrac{1}{12}}$

$\sf{\implies Let,\:\:C's\:one\:day\: work=\dfrac{1}{x}}$

$\tt{\implies Work\:done\:by\:_{(A+B+C)}=4\: days}$

• Here putting the value of A, B and C :-]

$\tt{\implies \dfrac{1}{8}+\dfrac{1}{12}+\dfrac{1}{x}=\dfrac{1}{4}}$

$\tt{\implies \dfrac{1}{x}=\dfrac{1}{4}-\dfrac{1}{8}-\dfrac{1}{12}}$

$\tt{\implies \dfrac{1}{x}=\dfrac{12-6-4}{48}}$

$\tt{\implies \dfrac{1}{x}=\dfrac{2}{48}}$

$\tt{\implies \dfrac{1}{x}=\dfrac{1}{24}}$

$\tt{\implies x=24}$

$\sf\large{Hence,}$

$\bf{\implies Work\:done\:by\:_{(C\:alone)}=24\: days}$