Question

Q8. John, Smith and Kate start at same time, same point and in same direction to run
around a circular ground. John completes a round in 250 seconds, Smith in 300
seconds and Kate in 150 seconds. Find after what time will they meet again at the
starting point?
a. 30 min
b. 25 min
c. 20 min
d. 15 min​

Answer 1

Least common multiple

Given: John, Smith and Kate start at same time, same point and in same direction to run around a circular ground. John completes a round in 250 seconds, Smith in 300 seconds and Kate in 150 seconds.

To find: After what time will they meet again at the starting point?

Solution:

We have to find the time, in which they meet after the start.

So we find the lcm (least common multiple) of three numbers.

• 250 = 2 × 5 × 5 × 5
• 300 = 2 × 2 × 3 × 5 × 5
• 150 = 2 × 3 × 5 × 5
• ∴ lcm (250, 300, 150) = 2 × 2 × 3 × 5 × 5 × 5
• = 1500

So we can say that they will meet after 1500 seconds = (1500 ÷ 60) minutes = 25 minutes.

Answer: Option b. 25 min