Questions & Answers

Question

Answers

A. 10

B. 11

C. 12

D. 23

Answer

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We will first assume that 2 hours have passed since the first taxi started from X. Let us consider one taxi starting from Y at this exact moment, at this moment of time there will be taxis at 10-minute intervals along the way. Now all the taxis that are in the way and started from X including the taxi that just reached Y and all the taxis that will start from X till the time this taxi from Y reaches X will cross this taxi from Y at some point of time. So, first we will calculate the number of taxis that are in the way.

As all the taxis are 10 minutes apart and it takes 2 hours for a one-way trip, there will be 11 taxis on the way. The taxi that reached Y and the taxi that will just begin at X are not counted as they are not enroute. After this taxi starts and takes 2 hours to reach X, 12 more taxis must have departed from X which will all cross this taxi from Y. So, in total 23 taxis coming from X will meet each taxi coming from Y and vice-versa.

We can also solve this problem using relative velocity. The relative velocity of each taxi with reference to a taxi coming from the other side. So, there are only 5-minute intervals in crossing each taxi. In the journey of 2 hours, there are 24 5-minute intervals. But in the last interval no taxi will cross, so we get the same answer i.e. 23.