Question

the forewheel of a tractor makes 120 revolution more than the rear wheel in going 720m if the diameter of the rear wheel is increased by 1 1/2 times the present diameter then the forewheel makes 20 revolutions more than the rear wheel in going the same distance find circumference of each wheel​

Answer 1

Let diameter of forewheel is d m and diameter rear-wheel is D m.

To cover 720m, number of revolution made by forewheel = 720/circumference of forewheel

= 720/πd

Similarly, To cover 720m, number of revolution made by rear-wheel = 720/πD

according to question,

720/πd - 720/πD = 120 revolutions

or, 1/d - 1/D = 120π/720

or, 1/d - 1/D = π/6 .........(1)

now, forewheel diameter is doubled, so new diameter of forewheel = 2d

and diameter of rear wheel is increased by 1.5 times so, new diameter of rear wheel = (3/2)D

now, To cover 720m, number of revolution of forewheel = 720/π(2d)

To cover 720m, number of revolution of rear wheel = 720/π(3/2)D

a/c to question,

720/π(2d) - 720/π(3/2)D = 20

or, 1/2d - 2/3D = 20π/720 = π/36 .......(2)

from equations (1) and (2),

-1/2D + 2/3D = π/12 - π/36

or, (-3 + 4)/6D = 2π/36

or, 1/6D = π/18

D = 3/π and d = 2/π

so, circumference of forewheel = πd = 2

circumference of rearwheel = πD = 3