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Five persons fire bullets at a target at an interval of 6, 7, 8, 9 and 12 seconds respectively. The number of times they would fire the bullets together at the target in an hour is
  • a)
    6
  • b)
    7
  • c)
    8
  • d)
    9
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Five persons fire bullets at a target at an interval of 6, 7, 8, 9 and...
Its a simple LCM based question. Take the LCM of 6,7,8,9 and 12 which comes out to be 504 seconds.
Divide 3600 seconds (1 hour) by 504 = It will be between 7 and 8. So the answer is (b).
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Most Upvoted Answer
Five persons fire bullets at a target at an interval of 6, 7, 8, 9 and...
Solution:

To find the number of times they would fire the bullets together at the target in an hour, we need to convert the time interval to the number of times they fire bullets in an hour.

Step 1: Convert the time interval to the number of times they fire bullets in an hour.

- Person 1: 1 bullet every 3600/6 = 600 seconds
- Person 2: 1 bullet every 3600/7 = 514.29 seconds
- Person 3: 1 bullet every 3600/8 = 450 seconds
- Person 4: 1 bullet every 3600/9 = 400 seconds
- Person 5: 1 bullet every 3600/12 = 300 seconds

Step 2: Find the LCM of the time intervals.

- LCM of 6, 7, 8, 9, and 12 = 2^3 x 3^2 x 7 = 504

Step 3: Find the number of times they fire bullets in an hour.

- Person 1: 3600/600 = 6 times
- Person 2: 3600/514.29 = 7 times
- Person 3: 3600/450 = 8 times
- Person 4: 3600/400 = 9 times
- Person 5: 3600/300 = 12 times

Step 4: Find the number of times they fire bullets together in an hour.

- We need to find the number of common multiples of 6, 7, 8, 9, and 12 within an hour, i.e., 3600 seconds.
- The number of times they fire bullets together in an hour = 3600/504 = 7.14 times
- Rounding down to the nearest integer, we get the answer as 7.

Therefore, the correct answer is option B (7).
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