Question

The diameter of rear wheel of a tractor is 1.5 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.

• A. $0.5m$
• B. $0.6m$
• C. $0.8$
• D. none of these

Answer 1

Answer: (A)

$0.5m$

We have
Diameter of the rear wheel D =1.5 m
Distance covered in one revolution = circumference of the wheel = $\pi D=1.5\pi$m
Now, Distance covered in 80 revolution $=80\times 1.5\pi =120\pi m$
Let $d$ be the diameter of the front wheel.
Now, Distance covered in one revolution by front wheel $=\pi d$ m
Now, Distance covered in 240 revolution by front wheel $=240\pi d$ m
Distance covered by front wheel in 240 revolution = Distance covered by rear wheel in 80 revolution
$=>240\pi d=120\pi$
$=>d=\frac{1}{2}$ m
$=>d=0.5$ m