L can run 1 km in 10 min while M can run it in 12 min. How many metres start can L give M in a km race, so that the race may end in a dead heat?

Time taken by L to run 1 km = 600 s
Time taken by M to run 1 km = 720 s
∴ L can give M a start of (720 - 600) = 120 s
∵ In 720 s, M runs 1000 m.
In 120 s M runs = (1000/720) x 120 = 500/3 m = 166²/₃ m
Hence, L can give a start of 166²/₃ m