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