Question

A toothed wheel of diameter 50 cm is attached to a smaller wheel of diameter 30 cm. Then the number of revolutions the smaller wheel will make when the larger one makes 30 revolution is

• A. $30$
• B. $50$
• C. $40$
• D. $60$

Answer 1

The correct option is B $50$

Given that diameters of wheels are $50$ cm and $30$ cm.

Distance covered by wheels in 1 revolution $=50\pi$ cm and $30\pi$ cm.

Let the number of revolutions by smaller wheel be $n$.

Then distance covered by larger wheel in $30$ revolution $=$ Distance covered by smaller wheel in $n$ revolutions that is:

$30\times 50\pi =n\times 30\pi \Rightarrow n=\frac{30\times 50\pi }{30\pi }\Rightarrow n=50$

Hence the smaller wheel makes $50$ revolutions.