The circumference of the back-sided wheel of a vehicle is 1 m greater than that of front side wheel. To travel 600 m, the front wheel rotates 30 times more than the back wheel. The circumference of the front wheel is :

Let the circumference of front wheel be x metres

Then, Circumference of rear wheel = (x - 1) metres
$$\eqalign{ & \therefore \frac{{600}}{x} - \frac{{600}}{{\left( {x + 1} \right)}} = 30 \cr & \Rightarrow \frac{1}{{x\left( {x + 1} \right)}} = \frac{1}{{20}} \cr & \Rightarrow x\left( {x - 1} \right) = 20 \cr & \Rightarrow \left( {{x^2} + x - 20} \right) = 0 \cr & \Rightarrow \left( {x + 5} \right)\left( {x - 4} \right) = 0 \cr & \Rightarrow x = 4\,m \cr} $$