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 when the larger one makes 30 revolutions?

Given,

Diameter of toothed larger wheel = 50 cm

Diameter of smaller wheel = 30 cm

Revolutions of larger wheel = 30

Distance covered by toothed larger wheel :

Distance in one revolution = circumference

C = 2πr = πd

C₁ = π × 50

Distance covered in 30 revolutions = 30 × 50π

= 1500π cm

Distance covered by smaller wheel:

C₂ = π × 30

Distance covered by smaller wheel in 1 revolution = 1 × 30π = 30π

Number of revolutions of the smaller vehicle

= $\dfrac{\text{Distance moved by toothed wheel in 30 revolutions}}{\text{Distance moved by smaller wheel in 1 revolution}}$

= $\dfrac{1500π}{30π}$

= 50.

Hence, number of revolutions = 50.