The diameters of front and rear wheels of a tractor are 80 cm and 2 m . . .

Question : The diameters of front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that rear wheel makes in covering a distance in which the front wheel makes 1400 revolutions?

Doubt by Vanshika

Solution : 

Diameter of front wheel (d) = 80 cm
Radius of front wheel (r) = 80/2 = 40 cm

Diameter of rear wheel (D) = 2 m 

Radius of rear wheel (R) = 2/2 = 1 m = 100 cm

Distance covered by front wheel in 1 rotation = 2πr

Distance covered by front wheel in 1400 rotation 

= 2πr×1400
= 2800πr — (1)

Let this distance is covered by rear wheel in 'n' rotation

Distance covered by real wheel in one rotation
= 2πR
Distance covered by real wheel in 'n' rotation
= 2πR×n
=2nπR — (2) 

Equating eq (1) and (2) 

2800πr=2nπR
2800π×40 = 2nπ×100
112000 = 200n

112000/200 = n
1120/2 = n

n = 560

Hence, the required number of revolution made by rear wheel is 560.