Answer :
Final answer:
Using ratio relationships given between runners A, B, and C, we can determine the times they take to complete a 100 metres race as 9 seconds, 10 seconds, and 10 seconds respectively. However, none of the given options match these computations and hence the answer should be 'Data Inadequate'.
Explanation:
The given problem is a typical one from races and relative speed in Mathematics. Here's how we find the time for each of them to run the 100 metres course. When A gives B 10 metres, it means when A runs 100 metres, B runs 90 metres. So, the time taken by A and B to complete the race are in the ratio 90:100 or 9:10. Similarly, when A gives C 20 metres, the time taken by A and C are in the ratio 80:100 or 4:5. Given that B can give C a 1 second headway in the 100 metres race, we have time taken by B and C in the ratio 9:10. The common ratio here for A,B and C is 9:10:10. Hence, their times could be 9k, 10k, and 10k for some common factor k. However, since B and C are given to have 1 sec difference, k has to be = 1sec. Therefore, A, B, and C take 9 sec, 10 sec, and 10 sec respectively to complete the race. Thus, the correct answer should be Data Inadequate as none of the options match with computed values.
Learn more about Race and Relative Speed here:
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