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49 pumps can empty a reservoir in days, working 8 hours a day. If 196 pumps are used for 5 hours each day, then the same work will be complete in ?

12 days
2 $2 \frac{1}{2}$ ${\text{2}}\frac{1}{2}$ days
3 $2 \frac{3}{5}$ ${\text{2}}\frac{3}{5}$ days
43 days

Answer:- 1

Explanation:-

Solution:

Let the required number of days be x
Then,
More pumps, Less days (Indirect proportion)
Less working hour/day, More days (Indirect proportion)

\begin{matrix} Pumps 196 : 49 \\ Working hour/day   5 : 8 \end{matrix}} :: \frac{13}{2} : x

$\left. \begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Pumps 196}}:49 \hfill \\ {\text{Working hour/day 5}}:8 \hfill \\ \end{gathered} \right\}::\frac{{13}}{2}:x$

\begin{aligned} ∴ 196 \times 5 \times x = 49 \times 8 \times \frac{13}{2} \\ \Leftrightarrow x = (49 \times 8 \times \frac{13}{2} \times \frac{1}{196 \times 5}) \\ \Leftrightarrow x = \frac{13}{5} \\ \Leftrightarrow x = 2 \frac{3}{5} \end{aligned}

$\eqalign{ & \therefore {\text{ }}196 \times 5 \times x = 49 \times 8 \times \frac{{13}}{2} \cr & \Leftrightarrow x = \left( {49 \times 8 \times \frac{{13}}{2} \times \frac{1}{{196 \times 5}}} \right) \cr & \Leftrightarrow x = \frac{{13}}{5} \cr & \Leftrightarrow x = 2\frac{3}{5} \cr}$

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\begin{aligned} ∴ 196 \times 5 \times x = 49 \times 8 \times \frac{13}{2} \\ \Leftrightarrow x = (49 \times 8 \times \frac{13}{2} \times \frac{1}{196 \times 5}) \\ \Leftrightarrow x = \frac{13}{5} \\ \Leftrightarrow x = 2 \frac{3}{5} \end{aligned}

$\eqalign{ & \therefore {\text{ }}196 \times 5 \times x = 49 \times 8 \times \frac{{13}}{2} \cr & \Leftrightarrow x = \left( {49 \times 8 \times \frac{{13}}{2} \times \frac{1}{{196 \times 5}}} \right) \cr & \Leftrightarrow x = \frac{{13}}{5} \cr & \Leftrightarrow x = 2\frac{3}{5} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

Let the required number of days be x
Then,
More pumps, Less days (Indirect proportion)
Less working hour/day, More days (Indirect proportion)

\begin{matrix} Pumps 196 : 49 \\ Working hour/day   5 : 8 \end{matrix}} :: \frac{13}{2} : x

$\left. \begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Pumps 196}}:49 \hfill \\ {\text{Working hour/day 5}}:8 \hfill \\ \end{gathered} \right\}::\frac{{13}}{2}:x$

\begin{aligned} ∴ 196 \times 5 \times x = 49 \times 8 \times \frac{13}{2} \\ \Leftrightarrow x = (49 \times 8 \times \frac{13}{2} \times \frac{1}{196 \times 5}) \\ \Leftrightarrow x = \frac{13}{5} \\ \Leftrightarrow x = 2 \frac{3}{5} \end{aligned}

$\eqalign{ & \therefore {\text{ }}196 \times 5 \times x = 49 \times 8 \times \frac{{13}}{2} \cr & \Leftrightarrow x = \left( {49 \times 8 \times \frac{{13}}{2} \times \frac{1}{{196 \times 5}}} \right) \cr & \Leftrightarrow x = \frac{{13}}{5} \cr & \Leftrightarrow x = 2\frac{3}{5} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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