P, Q, and R are racing on a circular track with a length of 'd' meters. During the race, P finishes 800 meters ahead of Q and 1200 meters ahead of R. Likewise, Q finishes 600 meters ahead of R. The race lasts for 'r' rounds. Based on the given information, which of the following values cannot be 'r', assuming the track length is an integer?

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.