Quantitative Aptitude :: Time and Distance - Discussion

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Explanation:
Let Annie's speed be X km/hr.
Its given, Mugil is thrice as fast as Annie. Therefore Mugil's speed be 3X km/hr.
Also it is said Agil is twice as fast as Mugil. Therefore, Agil's speed = Mugil's speed x 2 = 6X km/hr.
Therefore ratio of their speeds = 6X : 3X : X = 6 : 3 : 1
For a given distance, the time taken will be inversely proportional to speed.
Therefore, Ratio of times taken by the three friends Agil, Mugil and Annie = 1/6 : 1/3 : 1 = 1 : 2 : 6
If Annie takes 6 minutes then Mugil takes 2 minutes.
If Annie takes 54 minutes then Mugil takes [2/6 * 54]= 18 minutes.
Hence the answer is 18 minutes.