Question : A can run 250 m in 25 sec and B in 30 sec. How many metres start can A give to B in a 1 km race so that the race may end in a dead heat?
Option 1: 169.53 m
Option 2: 173.82 m
Option 3: 166.67 m
Option 4: 186.34 m
Correct Answer: 166.67 m
Solution :
A can run 250 m in 25 seconds.
⇒ A can run 1000 m in $\frac{25}{250} \times 1000$ = 100 seconds
B can run 250 m in 30 seconds.
⇒ B can run 1000 m in $\frac{30}{250} \times 1000$ = 120 seconds
Distance covered by B in an extra 20 seconds = $\frac{20}{120} \times 1000 = \frac{500}{3}$ = 166.67 m
Therefore, A beats B by 166.67 m.
For a dead-heat race, A must give B a start of 166.67 m.
Hence, the correct answer is 166.67 m.
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