The diameter of the front and rear wheels of a tractor are 80cm and 2m respectively. The number of revolutions that rear wheels will make in covering a distance in which the front wheel makes 1400 revolutions is:

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11200

760

560

360

answer is C.

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Detailed Solution

Diameter of front wheel of the tractor = 80cm
Now, Radius is half of the diameter. So,
Radius of front wheel of the tractor

= 802 = 40 c m

Now, circumference of circular wheel = 2πr
Substituting r = 40 in the above formula, we get
Circumference of the front wheel of the tractor

= 2 × 227 × 40 = 17607 c m

Now, in 1 revolution, the distance covered by the front wheel of the tractor = Circumference of the front wheel of the tractor

= 17607 c m

In 1400 revolutions, the distance covered by the front wheel of the tractor =

1400 × 17607 = 352000 c m

.
Similarly, Diameter of rear wheel of the tractor = 2m
Now, in 1 m, there are 100 cm. So,
Diameter of rear wheel of the tractor

= 2 × 100 = 200

cm.
Radius of rear wheel of the tractor =

2002 = 100 c m

Now, circumference of circular wheel = 2πr

Substituting r = 100 in the above formula, we get
Circumference of the rear wheel of the tractor

= 2 × 227 × 100 = 44007 c m

.
Now, the front and the rear wheel of the tractor will move together.
Therefore, when the front wheel has covered a distance of 352000cm
The number of revolutions made by the rear wheel

352000 × 44007 = 560

revolutions
The number of revolutions made by the rear wheel = 560 revolutions
Therefore, the number of revolutions that the rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions is 560 revolutions.

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