P, Q, and R are racing on a

Solution

ATQ, Length of race = d X r = 'dr' metres Distance covered by Q in the time that P takes to cover dr metres = (dr - 800) metres And, distance covered by R in the time that P takes to cover dr metres = (dr - 1200) metres And, distance covered by R in the time that Q takes to cover dr metres = (dr - 600) metres ATQ; {(dr - 800)/(dr - 1200)} = {dr/(dr - 600)} Or, (dr - 600) X (dr - 800) = dr X (dr - 1200) Or, dr2 - 600dr - 800dr + 480000 = dr2 - 1200dr Or, 480000 = 200dr So, dr = 2400 So, r = {2400/d} Among given options, only 18 is not a factor of 2400. So, all the other options are possible answers.