A 10 km race is organised at 800 m circular race course. P and Q are the contestants of the race. If the ratio of the speed of P and Q is 5 : 4, how many times will the winner overtake the loser?

Speed of P : Speed of Q = 5 : 4
Time taken by P to cover 5 rounds = Time taken by Q to cover 4 rounds
Distance covered by P in 5 rounds = 5 x (800/1000) = 4 km
Distance covered by Q in 4 rounds = 4 x (800/1000) = 16/5 km
In 5 rounds, P will overtake Q every time. It means that after covering 4 km, P will overtake Q one time .
∴ After covering 10 km P will overtake Q, = (1/4) x 10 = 2¹/₂ times