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P runs 1 km in 3 minutes and Q in 4 minutes 10 secs. How many metres start can P give Q in 1 kilometre race, so that the race may end in a dead heat?

210 metre
180 metre
220 metre
280 metre
Explanation:

P run 1 km in 3 minutes

Q run 1 km in 4 minutes 10 secs

$\text{=> Q runs 1 km in }\dfrac{25}{6}\text{ minutes}$

$\text{=> Q runs }\left(1 \times \dfrac{6}{25} \times 3\right)= \dfrac{18}{25} = 0.72\text{ km in 3 minutes}$

Hence, in a 1 km race, P can give Q $\left(1 - 0.72\right)$=0.28 km = 280 metre

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