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A toothed wheel of diameter 50 cm is attached to a smaller wheel of diameter 30 cm. How many revolutions will the smaller wheel make the larger one makes 15 revolutions ?

A toothed wheel of diameter 50 cm is attached to a smaller wheel of diameter 30 cm. How many revolutions will the smaller wheel make the larger one makes 15 revolutions ? Correct Answer 25

Distance covered by smaller wheel in 1 revolution :
$$\eqalign{ & = \left( {2\pi \times 15} \right)cm \cr & = \left( {30\pi } \right)cm \cr} $$
Distance covered by larger wheel in 1 revolution :
$$\eqalign{ & = \left( {2\pi \times 25} \right)cm \cr & = \left( {50\pi } \right)cm \cr} $$
Let,
$$k \times 30\pi = 15 \times 50\pi $$
Then,
$$k = \left( {\frac{{15 \times 50\pi }}{{30\pi }}} \right) = 25$$
∴ Required number of revolution = 25

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