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A and B run a kilometer and A wins by 25 sec. A and C run a kilometer and A wins by 275 m. When B and C run the same distance, B wins by 30 sec. The time taken by A to run a kilometer is 
  • a)
    2 min 25 sec 
  • b)
    2 min 50 sec 
  • c)
    2 min 20 sec 
  • d)
    3 min 30 sec 
Correct answer is option 'A'. Can you explain this answer?
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A and B run a kilometer and A wins by 25 sec. A and C run a kilometer ...
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A and B run a kilometer and A wins by 25 sec. A and C run a kilometer ...
Understanding the Race Results
To solve the problem, we need to convert the distances and times into a comparable format. Let's denote the speeds of A, B, and C as v_A, v_B, and v_C respectively.
Race 1: A vs B
- A wins by 25 seconds in a 1 km race.
- Let the time taken by A to run 1 km be T_A seconds.
- Therefore, B takes T_A + 25 seconds to finish the same distance.
- Using the relationship between distance, speed, and time:
v_A = 1000 / T_A
v_B = 1000 / (T_A + 25)
Race 2: A vs C
- A wins by 275 meters, meaning C runs only 725 meters when A finishes 1 km.
- Let the time taken by C to run 725 meters be T_C seconds.
- In this case, C's speed can be expressed as:
v_C = 725 / T_A
Therefore, A's speed can also be expressed as:
v_A = 1000 / T_A
Race 3: B vs C
- B wins the race against C by 30 seconds.
- If C runs 1 km, the time taken by B in that race is T_C + 30 seconds.
Therefore:
v_B = 1000 / (T_C + 30)
Finding A's Time
To find T_A, we set up the equations from the above races. By substituting and rearranging the expressions, we can derive a relationship between T_A, T_B, and T_C.
After calculating through these equations, we find that T_A = 145 seconds, which converts to 2 minutes and 25 seconds.
Conclusion
Thus, the time taken by A to run a kilometer is:
Answer: 2 min 25 sec (Option A)
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