Question

The diameter of rear wheel of a tractor i s1.5 m for covering some distance the rear wheel completes 80 revolutions and at the same time front wheel completes 240 revolutions. Find the diameter of front wheel.

Answer 1

Diameter of the rear wheel of the tractor = 1.5 m
Its radius = $\frac{1.5}{2}$ m
Number of revolutions completed by the rear wheel = 80
Number of revolutions completed by the front wheel = 240
Let the radius of the front wheel be r m.
Distance covered by the rear wheel = distance covered by the front wheel
$\Rightarrow$ Number of revolutions taken by the rear wheel × circumference of the rear wheel = number of revolutions taken by the front wheel × circumference of the front wheel
$\Rightarrow$ 80 × 2 ×$\pi$ × $\frac{1.5}{2}$= 240 × 2 × $\pi$× r
$\Rightarrow$ $\frac{80\times 2\times \mathrm{\pi }\times 1.5}{2\times 240\times 2\times \mathrm{\pi }}=r$
$\Rightarrow$ r = 0.25
∴ Radius of the front wheel = 0.25 m
and diameter of the front wheel = 0.25 × 2 m = 0.5 m