Three persons are walking around a ground. They take 20, 30 and 40 minutes to…
2020
Three persons are walking around a ground. They take 20, 30 and 40 minutes to complete one round. If they start from a single point together, they will meet again at that point after.
- A.
1 hour
- B.
1 1/2 hour
- C.
2 hour
- D.
2 1/2 hour
Attempted by 5 students.
Show answer & explanation
Correct answer: C
Complete Solution
To determine when the three persons will meet again at the starting point, we must find the smallest amount of time that is perfectly divisible by each person's individual round time. This requires calculating the Least Common Multiple (LCM).
Understand the requirement: Since each person completes a cycle in a fixed time, their meeting point occurs at a multiple of their respective times. To find the first time they meet again, we need the smallest common multiple.
Prime Factorization:
The round time for the first person is 20 minutes, which breaks down into 2 * 2 * 5.
The round time for the second person is 30 minutes, which breaks down into 2 * 3 * 5.
The round time for the third person is 40 minutes, which breaks down into 2 * 2 * 2 * 5.
Find the LCM: To find the LCM, we take the highest frequency of each prime factor present across the numbers:
We need three 2s (from the 40 minutes), one 3 (from the 30 minutes), and one 5 (shared by all).
LCM = 2 * 2 * 2 * 3 * 5 = 120 minutes.
Final conversion: 120 minutes divided by 60 minutes per hour equals 2 hours.