Question

Two cyclists start on a circular track from a given point but in opposite directions with speeds of 7 m/sec and 8 m/sec respectively. If the circumference of the circle is 300 metres, after what time will they meet at the starting point for the first time?

• A. 20 sec
• B. 100 sec
• C. 300 sec
• D. 200 sec

Hint:

To find when multiple events coincide, calculate the least common multiple (LCM) of the time periods involved.

Answer 1

The Correct Option is C

Let the time taken by the two cyclists to reach the starting point be calculated. Since the circumference of the circle is 300 metres, the time taken for each cyclist to complete one full cycle is: - Cyclist A: \( \frac{300}{7} \) seconds - Cyclist B: \( \frac{300}{8} \) seconds They will meet at the starting point when the least common multiple (LCM) of these two times is achieved. Thus, we find the LCM of \( \frac{300}{7} \) and \( \frac{300}{8} \), which is \( 300 \) seconds. Hence, the time taken for both cyclists to meet at the starting point for the first time is \( 300 \) seconds.