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3 pumps , working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day ?

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Answer:- 1

Explanation:-

Solution:

Let the required number of working hours per day be x
More pumps, Less working hours per day (Indirect proportion)
Less days, More working hours per day (Indirect proportion)

\begin{matrix} Pumps  4 : 3 \\ Days 1 : 2 \end{matrix}} :: 8 : x

$\left. \begin{gathered} {\text{Pumps 4}}:3 \hfill \\ \,\,\,\,\,\,{\text{Days 1}}:2 \hfill \\ \end{gathered} \right\}::8:x$

\begin{aligned} ∴ 4 \times 1 \times x = 3 \times 2 \times 8 \\ \Leftrightarrow x = \frac{(3 \times 2 \times 8)}{(4)} \\ \Leftrightarrow x = 12 \end{aligned}

$\eqalign{ & \therefore {\text{ }}4 \times 1 \times x = 3 \times 2 \times 8 \cr & \Leftrightarrow x = \frac{{\left( {3 \times 2 \times 8} \right)}}{{\left( 4 \right)}} \cr & \Leftrightarrow x = 12 \cr}$

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\begin{aligned} ∴ 4 \times 1 \times x = 3 \times 2 \times 8 \\ \Leftrightarrow x = \frac{(3 \times 2 \times 8)}{(4)} \\ \Leftrightarrow x = 12 \end{aligned}

$\eqalign{ & \therefore {\text{ }}4 \times 1 \times x = 3 \times 2 \times 8 \cr & \Leftrightarrow x = \frac{{\left( {3 \times 2 \times 8} \right)}}{{\left( 4 \right)}} \cr & \Leftrightarrow x = 12 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

Let the required number of working hours per day be x
More pumps, Less working hours per day (Indirect proportion)
Less days, More working hours per day (Indirect proportion)

\begin{matrix} Pumps  4 : 3 \\ Days 1 : 2 \end{matrix}} :: 8 : x

$\left. \begin{gathered} {\text{Pumps 4}}:3 \hfill \\ \,\,\,\,\,\,{\text{Days 1}}:2 \hfill \\ \end{gathered} \right\}::8:x$

\begin{aligned} ∴ 4 \times 1 \times x = 3 \times 2 \times 8 \\ \Leftrightarrow x = \frac{(3 \times 2 \times 8)}{(4)} \\ \Leftrightarrow x = 12 \end{aligned}

$\eqalign{ & \therefore {\text{ }}4 \times 1 \times x = 3 \times 2 \times 8 \cr & \Leftrightarrow x = \frac{{\left( {3 \times 2 \times 8} \right)}}{{\left( 4 \right)}} \cr & \Leftrightarrow x = 12 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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