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August 9th, 2019, 07:37 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 476 Thanks: 1  What is the use of finding time ratio in this problem?
Dipak goes to his office, covering half of the distance by auto & rest by metro; total time taken by him to cover complete distance is 50 min. If he covers complete distance by metro, it would take 35 mins to reach the office. On a particular day, he goes to his office & returns by auto; find total time taken in complete journey. Solution: Half the distance by auto and half by metro  total time > 50 min. Total distance by metro > 35 min. Half the distance by metro > 17.5 min...(1). So half the distance by auto > 5017.5 = 32.5 min...(2). Time ratio when distance is same... auto : metro : 32.5:17.5 = 13:7. Now it took 35 mins to cover total distance by metro, so it takes 65 min by auto. What is the use of finding time ratio in this problem? Last edited by skipjack; August 9th, 2019 at 11:04 PM. 
August 9th, 2019, 11:41 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,026 Thanks: 2257 
There's no need to find the time ratio. The first sentence implies that doing the entire outward leg by auto and the entire return leg (using the same length route) by metro would take 100 mins overall. The second sentence implies that doing just one of those legs by metro would take 35 mins. Hence doing one leg by auto would take 65 mins. However, the question asks for the time that would be taken using auto for the complete journey, i.e. both legs, so the answer should be 130 mins. The given solution went wrong where it stated "it took 35 mins to cover total distance by metro", because it was stated that just the leg to reach the office would take 35 minutes by metro, not both legs combined. 

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