Question

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

Answer 1

Answer:

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Step-by-step explanation:

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