### Solution:

Let the diameter of the fore wheel of the tractor be .The diameter of the rear wheel of the tractor be .

So the circumference of the fore wheel be The circumference of the rear wheel be Now since the tractor is travelling a distance of , so the number of revolution made by fore wheel will be And the number of revolution made by rear wheel will be It is also said that fore wheel of a tractor makes revolutions more than the rear wheel in while going , hence we can write this as

This can be written as

Now it is said that the diameter of the fore wheel is doubled and the diameter of the rear wheel is increased by times.

So to cover , the number of revolution made by new fore wheel will be And the number of revolution made by new rear wheel will be Now it is said when the diameter of the fore wheel is doubled and the diameter of the rear wheel is increased by times the fore wheel makes revolutions more than the rear wheel, hence we can write this as

Now multiply the denominator of the equation (1) by 2 and subtract equation (2) from it, we get

Now substitute the value of D in equation (1), we get

Now the circumference of the fore wheel is given as

= 2

And also the circumference of the rear wheel is given as

Therefore the circumference of the fore wheel and rear wheel is and respectively.

Hence, Option (1) is the correct Ans:.