Question

The diameter of the rear wheel of a tractor is 1.5 m for covering some distance the rear wheel completes 80 revolutions and at the same time the front wheel completes 240 revolutions. Find the diameter of the front wheel.
(A) 0.5 m
(B) 0.6 m
(C) 0.8
(D) None of these

Answer 1

Hint: We should know that the circumference of a circle is defined as the linear distance around the circle. In simple words, we can say that if a circle is opened to the form of a straight line then the length of that line will be the circumference of the circle. Based on this concept we have to solve this question.

Complete step by step answer
We have,
The diameter of the rear wheel D = 1.5 m
The distance covered in one revolution = circumference of the wheel = $\pi D$= 1.5 $\pi$m
Now the distance covered in 80 revolution = $80 \times 1.5\pi = 120\pi m$
Let us consider that the diameter of the front wheel is d.
So the distance covered in one revolution by the front wheel = $\pi d$m
And the distance covered in 240 revolution by the front wheel = $240\pi d$m.
The distance covered by the front wheel in 240 revolution = Distance covered by the rear wheel in 80 revolution.
$\Rightarrow 240\pi d = 120\pi$
$\Rightarrow d = \dfrac{1}{2}m$
$\Rightarrow d = 0.5m$

Hence the correct answer is option A.

Note To solve the questions which consist of the circumference we need to know that if the value of the diameter of the circle is given then we can multiply pi to the diameter value to get the value of the circumference. To find the revolution we need to use the formula where we multiply 2 with the value of pi and r. The value of pi can be 3.14 and r is the radius of the wheel.