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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)
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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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 isa)2 min 25 secb)2 min 50 secc)2 min 20 secd)3 min 30 secCorrect answer is option 'A'. Can you explain this answer? for Teaching 2025 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about 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 isa)2 min 25 secb)2 min 50 secc)2 min 20 secd)3 min 30 secCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Teaching 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 isa)2 min 25 secb)2 min 50 secc)2 min 20 secd)3 min 30 secCorrect answer is option 'A'. Can you explain this answer?.
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 isa)2 min 25 secb)2 min 50 secc)2 min 20 secd)3 min 30 secCorrect answer is option 'A'. Can you explain this answer? for Teaching 2025 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about 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 isa)2 min 25 secb)2 min 50 secc)2 min 20 secd)3 min 30 secCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Teaching 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 isa)2 min 25 secb)2 min 50 secc)2 min 20 secd)3 min 30 secCorrect answer is option 'A'. Can you explain this answer?.
Solutions for 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 isa)2 min 25 secb)2 min 50 secc)2 min 20 secd)3 min 30 secCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Teaching.
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