Question
49 pumps can empty a reservoir in $$6\frac{1}{2}$$ days, working 8 hours a day. If 196 pumps are used for 5 hours each day, then the same work will be complete in ?
Answer: Option C
Let the required number of days be x
Then,
More pumps, Less days (Indirect proportion)
Less working hour/day, More days (Indirect proportion)
\[\left. \begin{gathered}
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Pumps 196}}:49 \hfill \\
{\text{Working hour/day 5}}:8 \hfill \\
\end{gathered} \right\}::\frac{{13}}{2}:x\]
$$\eqalign{
& \therefore {\text{ }}196 \times 5 \times x = 49 \times 8 \times \frac{{13}}{2} \cr
& \Leftrightarrow x = \left( {49 \times 8 \times \frac{{13}}{2} \times \frac{1}{{196 \times 5}}} \right) \cr
& \Leftrightarrow x = \frac{{13}}{5} \cr
& \Leftrightarrow x = 2\frac{3}{5} \cr} $$
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Let the required number of days be x
Then,
More pumps, Less days (Indirect proportion)
Less working hour/day, More days (Indirect proportion)
\[\left. \begin{gathered}
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Pumps 196}}:49 \hfill \\
{\text{Working hour/day 5}}:8 \hfill \\
\end{gathered} \right\}::\frac{{13}}{2}:x\]
$$\eqalign{
& \therefore {\text{ }}196 \times 5 \times x = 49 \times 8 \times \frac{{13}}{2} \cr
& \Leftrightarrow x = \left( {49 \times 8 \times \frac{{13}}{2} \times \frac{1}{{196 \times 5}}} \right) \cr
& \Leftrightarrow x = \frac{{13}}{5} \cr
& \Leftrightarrow x = 2\frac{3}{5} \cr} $$
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