A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. If the smaller wheel has made 21 revolutions, what will be the number of revolutions made by the larger wheel?
15
12
21
9
Explanation:
Let the number of revolutions made by the larger wheel be $x$
More cogs, less revolutions (Indirect proportion)
Hence we can write as
(cogs) 6 : 14 :: $x$ : 21
$\Rightarrow 6 \times 21 = 14 \times x\\$
$\Rightarrow 6 \times 3 = 2 \times x\\$
$\Rightarrow 3\times 3 = x\\$
$\Rightarrow x = 9$