The time intervals at which the five persons fire the bullets are 6, 7, 8, 9, and 12 seconds.

To find how often they will fire together in an hour, we need to find the least common multiple (LCM) of the time intervals. The LCM of 6, 7, 8, 9, and 12 gives the interval at which they will fire together.

Find the prime factorization of each number:

$6 = 2 \times 3$ $7 = 7$ $8 = 2^3$ $9 = 3^2$ $12 = 2^2 \times 3$ The LCM is obtained by taking the highest powers of all primes that appear:

The highest power of 2: $2^3$ (from 8) The highest power of 3: $3^2$ (from 9) Highest power of 7: 7 (from 7) LCM = $2^3 \times 3^2 \times 7 = 8 \times 9 \times 7 = 504$ seconds. This means they will all fire together once every 504 seconds.

To find how many times they fire together in an hour (3600 seconds), divide 3600 by 504: $3600 \div 504 = 7.14$.

Since they fire together once at the start, and the next time will be after 504 seconds, they will fire together 7 times in an hour.

Thus, the correct answer is B. 7.

NOTE: UPSC answer key considered both options B and C as correct.