[9] A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. If the smaller wheel has made 21 r

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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?

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

$\Rightarrow 6 \times 21 = 14 \times x\\$

$\Rightarrow 6 \times 3 = 2 \times x\\$

$\Rightarrow 3\times 3 = x\\$

$\Rightarrow x = 9$

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