Question

Three pipes A B and C can fill a swimming pool in 6 hours. After working on it together for 2 hours, C is closed and A and B fill the remaining part in 7 hours. Find the number of hours taken by C alone to fill the swimming pool.​

Answer 1

Answer:

The pipe C alone can fill the tank in 14 hours

Step-by-step explanation:

Given as :

The three pipes a , b , c can fill the pipes in 6 hours They work for 2 hours After that c pipe is close and a , b finish remaining work Now, According to question In 1 hour pipes ( a + b + c ) fill of the tank ∴ In 2 hour pipes ( a + b + c ) fill =   of the tank Remaining ( 1 -  ) =  part is filled by pipes a and b in 7 hours ∴ The whole tank is filled by a and b in 7 × =   hours ∴ In 1 hour pipes A and b fill the tank in hours ∴ In 1 hour pipes C alone can fill the tank in - hours Or,  In 1 hour pipes C alone can fill the tank in =   Or, In 1 hour pipes C alone can fill the tank in 14 hours Hence The pipe C alone can fill the tank in 14 hours .

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Answer 2

Solution :-

$\begin{gathered} \mathsf{ {Part \: time \: in \: 2 \: hours= \frac{2}{6} = \frac{1}{3} }} \\ \end{gathered}$

$\begin{gathered}\Large\mathsf{Remaining\: part=(1 - \frac{1}{3}) } = \frac{2}{3} \\\end{gathered}$

$\begin{gathered}\Large\mathsf{ \therefore \: (A + B) \prime s \: 7 \: hours \: work = \frac{2}{3} }\\\end{gathered}$

$\begin{gathered}\Large\mathsf{ (A + B) \prime s \: 1 \: hour\: work = \frac{2}{21} }\\\end{gathered}$

$\begin{gathered}\large\mathsf{∴ C's \: hour's \: work= {(A+B+C)'s \: 1 \: hour's \: work} -{(A+B)'s \: 1 \: hour's \: work}}\\\end{gathered}$

$\begin{gathered}\Large\dashrightarrow\mathsf{( \frac{1}{6} - \frac{2}{21}) = \frac{1}{14} }\\\end{gathered}$

• ∴ C alone can fill the tank in 14 hours .

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