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 ?

Answer: Option D

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)
$$\begin{array}{c}\text{Carpenters 12}:18\text{hfill}\\ \text{Hours per day 6}:8\text{hfill}\\ \text{Days 24}:\text{36}\text{hfill}\end{array}\}::460:x$$
$$\begin{array}{rl}& \therefore 12\times 6\times 24\times x=18\times 8\times 36\times 460\\ & \iff x=\frac{\left(18\times 8\times 36\times 460\right)}{\left(12\times 6\times 24\right)}\\ & \iff x=1380\end{array}$$
∴ Required number of chairs = 1380