Five persons fire bullets at a target at an interval of 6, 7, 8, 9 and 12 seconds respectively. The number of

Question

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

Accepted Answer

The problem requires finding the Least Common Multiple (LCM) of the given intervals to determine when all five persons fire together.

1.  Calculate the LCM of the firing intervals: 6, 7, 8, 9, and 12 seconds.
    *   Prime factorization:
        *   6 = 2 x 3
        *   7 = 7
        *   8 = 2^3
        *   9 = 3^2
        *   12 = 2^2 x 3
    *   LCM = 2^3 x 3^2 x 7 = 8 x 9 x 7 = 72 x 7 = 504 seconds.
    This means they will all fire together every 504 seconds.

2.  Convert the total time (1 hour) into seconds.
    *   1 hour = 60 minutes = 60 x 60 seconds = 3600 seconds.

3.  Divide the total time by the LCM to find how many times they fire together within that hour.
    *   Number of times = Total time / LCM = 3600 seconds / 504 seconds.
    *   3600 / 504 = 7.142...

4.  Since we are looking for the number of complete instances within the hour, we take the integer part of the result.
    *   The integer part is 7.
    This implies that they will fire together 7 times within the hour (at 504s, 1008s, 1512s, 2016s, 2520s, 3024s, 3528s). This interpretation typically excludes the initial firing at time t=0 if the "in an hour" refers to the duration after the start.

Therefore, they would fire the bullets together at the target 7 times in an hour.

The final answer is B

Answer

6

Answer

7

Answer

8

Answer

9

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

Explanation

Related questions