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Working 8 hours a day, 12 men can do a work in 30 days. Working 4 hours a day, 18 men can do work in ?

130 days
240 days
345 days
450 days

Answer:- 1

Explanation:-

Solution:

Let the required number of days be x
Less working hours, More days (Indirect Proportion)
More men, Less days (Indirect Proportion)

\begin{matrix} Working hours 4 : 8 \\ Men 18 : 12 \end{matrix}} :: 30 : x

$\left. \begin{gathered} {\text{Working hours 4}}:8 \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Men 18}}:12 \hfill \\ \end{gathered} \right\}::30:x$

\begin{aligned} ∴ 4 \times 18 \times x = 8 \times 12 \times 30 \\ \Leftrightarrow x = \frac{(8 \times 12 \times 30)}{(4 \times 18)} \\ \Leftrightarrow x = 40 \end{aligned}

$\eqalign{ & \therefore {\text{ }}4 \times 18 \times x = 8 \times 12 \times 30 \cr & \Leftrightarrow x = \frac{{\left( {8 \times 12 \times 30} \right)}}{{\left( {4 \times 18} \right)}} \cr & \Leftrightarrow x = 40 \cr}$

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\begin{aligned} ∴ 4 \times 18 \times x = 8 \times 12 \times 30 \\ \Leftrightarrow x = \frac{(8 \times 12 \times 30)}{(4 \times 18)} \\ \Leftrightarrow x = 40 \end{aligned}

$\eqalign{ & \therefore {\text{ }}4 \times 18 \times x = 8 \times 12 \times 30 \cr & \Leftrightarrow x = \frac{{\left( {8 \times 12 \times 30} \right)}}{{\left( {4 \times 18} \right)}} \cr & \Leftrightarrow x = 40 \cr}$ ", "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
Less working hours, More days (Indirect Proportion)
More men, Less days (Indirect Proportion)

\begin{matrix} Working hours 4 : 8 \\ Men 18 : 12 \end{matrix}} :: 30 : x

$\left. \begin{gathered} {\text{Working hours 4}}:8 \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Men 18}}:12 \hfill \\ \end{gathered} \right\}::30:x$

\begin{aligned} ∴ 4 \times 18 \times x = 8 \times 12 \times 30 \\ \Leftrightarrow x = \frac{(8 \times 12 \times 30)}{(4 \times 18)} \\ \Leftrightarrow x = 40 \end{aligned}

$\eqalign{ & \therefore {\text{ }}4 \times 18 \times x = 8 \times 12 \times 30 \cr & \Leftrightarrow x = \frac{{\left( {8 \times 12 \times 30} \right)}}{{\left( {4 \times 18} \right)}} \cr & \Leftrightarrow x = 40 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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