If 12 carpenters, working 6 hours a day, can make 460 chairs in 24 days, how many chairs will 18 carpenters make in 36 days, each working 8 hours a day ?

Solution (By Examveda Team)

Let the required number of chairs be x
Then, More carpenters, More chairs (Direct proportion)
More hours per day, More chairs (Direct proportion)
More days, More chairs (Direct proportion)
\[\left. \begin{gathered} \,\,\,\,{\text{Carpenters 12}}:18 \hfill \\ {\text{Hours per day 6}}:8 \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Days 24}}:{\text{36}} \hfill \\ \end{gathered} \right\}::460:x\]
$$\eqalign{ & \therefore {\text{ }}12 \times 6 \times 24 \times x = 18 \times 8 \times 36 \times 460 \cr & \Leftrightarrow x = \frac{{\left( {18 \times 8 \times 36 \times 460} \right)}}{{\left( {12 \times 6 \times 24} \right)}} \cr & \Leftrightarrow x = 1380 \cr} $$
∴ Required number of chairs = 1380