Question

The forewheel of a tractor makes 120 revolutions more than the rear wheel in going 720m.if the diameter of the forewheel is doubled and the diameter of the rear wheel is increased by 1.5 times the present diameter then the forewheel makes 20 revolutions more than the rear wheel going same distance.find the 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

a/c 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

Answer 2

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

a/c 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