When Will Three Cyclists Meet Again on a Circular Field?

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: A circular field has a circumference of 360 km. Three cyclists start together and can cycle 48 km, 60 km and 72 km a day around the field. When will they meet again?

Step 1: Find the Time Taken by Each Cyclist to Complete One Round

Time taken by first cyclist = 360 ÷ 48 = 7.5 days

Time taken by second cyclist = 360 ÷ 60 = 6 days

Time taken by third cyclist = 360 ÷ 72 = 5 days

Step 2: Convert the Times into Fractions

7.5 days = 15 / 2 days

6 days = 6 / 1 days

5 days = 5 / 1 days

Step 3: Find the LCM of the Time Periods

LCM of 15/2, 6 and 5

= LCM of (15, 6, 5) ÷ HCF of (2, 1, 1)

LCM of (15, 6, 5) = 30

HCF of (2, 1, 1) = 1

LCM = 30 ÷ 1 = 30

Final Answer

∴ The three cyclists will meet again after 30 days.

Conclusion

Thus, by finding the time taken by each cyclist to complete one round and then calculating their LCM, we conclude that all three cyclists will meet again after 30 days.