Let P,Q and R be the three runners.
• Let P's speed be x m/sec
• Let Q's speed be y m/sec
• Let R's speed be z m/sec
• According to the question, P wins by 1 minute over Q and by 375 m over R.
• Also, Q wins by 30 seconds over R.
• We can write the following equations using the above information:

• 1 minute = 60 seconds
• P's distance covered = Q's distance covered + 60 seconds * x m/sec
• P's distance covered = R's distance covered + 375 m
• Q's distance covered = R's distance covered + 30 seconds * y m/sec

• From the first equation, we get:
• 60 seconds * x m/sec = 60 seconds * y m/sec + 375 m
• x m/sec = y m/sec + 375/60 m/sec
• From the second equation, we get:
• x m/sec = z m/sec + 375/60 m/sec
• z m/sec = x m/sec - 375/60 m/sec
• Substituting the value of x m/sec from the first equation, we get:
• z m/sec = y m/sec + 375/60 m/sec - 375/60 m/sec
• z m/sec = y m/sec

• We can calculate the individual speeds of the runners using the above equations.
• x m/sec = y m/sec + 375/60 m/sec
• x m/sec = z m/sec + 375/60 m/sec
• y m/sec = z m/sec
• x m/sec = 2y m/sec + 375/60 m/sec
• x = 2y + 375/60
• y = x - 375/60
• z = x - 375/60

• From the above equations, we can calculate the individual speeds of the runners.
• x = 2(x - 375/60) + 375/60
• x = 3x - 375/30
• 4x = 375/30
• x = 375/120 m/sec
• y = x - 375/60 = 375/120 - 375/60 = 375/240 m/sec
• z = x - 375/60 = 375/120 - 375/60 = 375/240 m/sec

• We can calculate the time taken by each runner to run a kilometre by using the formula:
• Time taken = Distance/Speed
• Time taken by P = 1000/ x = 1000/ 375/120 = 150 seconds
• Time taken by Q = 1000/ y = 1000/ 375/240 = 210 seconds
• Time taken by R = 1000/ z = 1000/ 375/240 = 240 seconds

Hence, the time taken by each runner to run a kilometre is 150 seconds, 210 seconds and 240 seconds respectively.

Thus, the correct answer is option A. 150 sec, 210 sec, 240 sec.

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