Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

Explanation:-

Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
$$\left. \begin{gathered} {\text{Machines}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{4}}:3 \hfill \\ {\text{Time(in min}}{\text{.)}}\,\,{\text{1}}:2 \hfill \\ \end{gathered} \right\}::270:x$$
$$\eqalign{ & \therefore 6 \times 1 \times x = 10 \times 4 \times 270 \cr & \Rightarrow x = \frac{{\left( {10 \times 4 \times 270} \right)}}{{\left( 6 \right)}} \cr & \Rightarrow x = 1800 \cr}$$