Separated friends
Gloria is attending a concert where people have just started to pour in. She is oblivious of her friend Jack dropping by, few steps away in the entrance zone. Gloria is only the fifth person from the entrance gate while Jack is the fifteenth person from end of the line. If half of the people between Gloria and Jack were removed, the line would be cut by a third and Jack may be able to spot Gloria. How many people are in the queue for the concert?
The answer is 60.
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1 solution
Let the total line be of N people. Half the number of people between Gloria and Jack are a third of the total line. Thus, number of people between Jack and Gloria are two-thirds of the total line.
Gloria's position from start, P1 = 5 Jack's position from start, P2 = N - 15 + 1 = N - 14 No of people between Gloria and Jack = P2 - P1 - 1 = N - 14 - 5 - 1 = 3 2 N
Note that we counted the people as difference of their positions minus 1. To support the reason for doing so, suppose two people are consecutive in a line. Assume at ninth and tenth place. Then there is not a single person between them, but the difference of their positions is 1. That is why, we need to subtract 1.
Now, N - 20 = 3 2 N which gives N = 60