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 :

Answer: Option B

Solution

Answer: Option B

Solution:

Let the circumference of front wheel be x metres

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