Question

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 made by the larger wheel is

• A. $4$
• B. $9$
• C. $12$
• D. $49$

Answer 1

The correct option is B $9$

Let the required number of revolutions made by larger wheel be $x$.
We know,

More cogs$⟹$ Less revolutions

So, it is Indirect Proportion

$\therefore 14:6::21:x$

$\Rightarrow 14\times x=6\times 21$
$\Rightarrow x=\frac{6\times 21}{14}$
$\Rightarrow x=9$

Hence, number of revolutions made by larger wheel is $9$