The fore wheel of a tractor makes revolutions more than the rear wheel going meters. If the diameter of the fore wheel is doubled and the diameter of the rear wheel is increased by times the present diameter, then the fore wheel makes revolutions more than the rear wheel in going the same distance. Find the circumference of each wheel.

# The fore wheel of a tractor makes revolutions more than the rear wheel going meters. If the diameter of the fore wheel is doubled and the diameter of the rear wheel is increased by times the present diameter, then the fore wheel makes revolutions more than the rear wheel in going the same distance. Find the circumference of each wheel.

1. A
2, 3
2. B
4, 5
3. C
5, 6
4. D
1, 2

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### 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:.

## Related content

 Area of Square Area of Isosceles Triangle Pythagoras Theorem Triangle Formula Perimeter of Triangle Formula Area Formulae Volume of Cone Formula Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)