A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:

Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
$$\eqalign{ & \therefore 14:6::21:x \cr & \Rightarrow 14 \times x = 6 \times 21 \cr & \Rightarrow x = \frac{{6 \times 21}}{{14}} \cr & \Rightarrow x = 9 \cr} $$