12 persons can do a piece of work in 4 days. How many persons are required to complete 8 times the work in half the time ?

1144
2180
3190
4192

Answer:- 1

Explanation:-

Solution:

Let the required number of persons be x
Less days , More persons (Indirect proportion)
More work , More persons (Direct proportion)

\begin{matrix} Days 2 : 4 \\ Work 1 : 8 \end{matrix}} :: 12 : x

$\left. \begin{gathered} \,{\text{Days 2}}:4 \hfill \\ {\text{Work 1}}:8 \hfill \\ \end{gathered} \right\}::12:x$

\begin{aligned} ∴ 2 \times 1 \times x = 4 \times 8 \times 12 \\ \Leftrightarrow x = \frac{(4 \times 8 \times 12)}{(2)} \\ \Leftrightarrow x = 192 \end{aligned}

$\eqalign{ & \therefore \,2 \times 1 \times x = 4 \times 8 \times 12 \cr & \Leftrightarrow x = \frac{{\left( {4 \times 8 \times 12} \right)}}{{\left( 2 \right)}} \cr & \Leftrightarrow x = 192 \cr}$

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\begin{aligned} ∴ 2 \times 1 \times x = 4 \times 8 \times 12 \\ \Leftrightarrow x = \frac{(4 \times 8 \times 12)}{(2)} \\ \Leftrightarrow x = 192 \end{aligned}

$\eqalign{ & \therefore \,2 \times 1 \times x = 4 \times 8 \times 12 \cr & \Leftrightarrow x = \frac{{\left( {4 \times 8 \times 12} \right)}}{{\left( 2 \right)}} \cr & \Leftrightarrow x = 192 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

Let the required number of persons be x
Less days , More persons (Indirect proportion)
More work , More persons (Direct proportion)