Question

The fore wheel of a
wheel of a tractor makes
120 revolutions more than the rear wheel
in going 720 m. If the diameter of the fore
wheel is doubled and the diameter of the
rear wheel is increased by 1and half times the present diameter, then the fore wheel makes 20 revolutions more than the rear wheel in going the same distance. Find the circumference of each wheel​

Answer 1

Answer:

Step-by-step explanation:

Let the  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

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 the  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

so,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