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 ?

A. 144

B. 180

C. 190

D. 192

Answer: Option D

Solution(By Examveda Team)

Let the required number of persons be x
Less days , More persons (Indirect proportion)
More work , More persons (Direct proportion)
\[\left. \begin{gathered} \,{\text{Days 2}}:4 \hfill \\ {\text{Work 1}}:8 \hfill \\ \end{gathered} \right\}::12:x\]
$$\eqalign{ & \therefore \,2 \times 1 \times x = 4 \times 8 \times 12 \cr & \Leftrightarrow x = \frac{{\left( {4 \times 8 \times 12} \right)}}{{\left( 2 \right)}} \cr & \Leftrightarrow x = 192 \cr} $$