X and Y run a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3:2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)?

Correct Answer: (B) 3

The race length is 3 km = 3000 m on a circular track of 300 m. When the faster runner X finishes the 3000 m race, the slower runner Y (running at $\frac{2}{3}$$\frac{2}{3}$ of X's speed) covers $\frac{2}{3}\times 3000=2000\text{ m}$$\frac{2}{3}$ $\times$ 3000 = 2000$\text{ m}$. The relative distance gained by X over Y is $3000 - 2000 = 1000$$\text{ m}$. Because X laps Y each time X gains a full 300 m lap, the number of passing events is $\lfloor$$\frac{1000}{300}$ \rfloor = 3 times (at relative leads of 300 m, 600 m, and 900 m).