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Quantitative Reasoning – How many times do they meet in a circular race!

PSA 2014_XI_Q8. Tahir and Gagan rode in a 150 km bicycle race. The race was held on a 20 km track. Tahir averaged 30 km/h while Gagan averaged 15 km/h.
How many times did Tahir pass Gagan during the race ?

1 ) 2
2 ) 3
3 ) 4
4 ) 5

Ans: It is evident that race is on a circular track of 20km. As soon as Tahir and Gagan start the race Tahir gets ahead as he has higher speed than Gagan. Freeze the scene just after a moment after the race starts; we should be able to visualize that Tahir has got ahead and he sees that to meet Gagan he has to cover the entire 20 km. To meet once (or to cover this 20 km), Tahir will take the below given time:

Distance/Relative speed = 20/(30-15) hrs = 1 hr 20 minutes. [We’re to take relative speed as Gagan is also moving in the same direction so effectively the time is more].

Now, to completed the race, Tahir takes 150/30 = 5 hrs.

Since, both meet after every 1 hr 20 minutes, they could meet at best 3 times (3* 1hr20 minutes = 4 hrs). They can’t meet the 4th time as Tahir would have finished the race and stopped after 5 hrs.

Addition question to solve:

At what point(s) do they meet each other?

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