Question : In a 200-metre linear race, if A gives B a start of 25 m, A wins the race by 10 seconds. Alternatively, if A gives B a start of 45 m, the race ends in a dead heat. How long does A take to run 200 m?
Option 1: 78 seconds
Option 2: 77 seconds
Option 3: 78.5 seconds
Option 4: 77.5 seconds
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Correct Answer: 77.5 seconds
Solution : Given: In a 200 m linear race, if A gives B a start of 25 m, A wins by 10 seconds. Alternatively, if A gives B a start of 45 m, the race ends in a dead heat. So, the additional 20 m start given to B compensates for the 10 seconds. i.e., B runs 20 m in 10 seconds. Hence, B will take 100 seconds to run 200 m. Also, A gives B a start of 45 m. Since B runs 20 m in 10 seconds, 45 m will be covered in 22.5 seconds. A will take 22.5 seconds less than B, or, 100 – 22.5 = 77.5 seconds, to complete the race. Hence, the correct answer is 77.5 seconds.
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