Practice Problem - 5 : Seven children A, B, C, D, E, F and G started walking from the same point at the same time, with speeds in the ratio of 1 : 2 : 3 : 4 : 5 : 6 : 7 respectively and they are running around a circular park. Each of them carry flags of different colours and whenever two or more children meet, they place their respective flag at that point. However nobody places more than 1 flag at a same point. They are running in anti-clockwise direction. How many flags will be there in total, when there will be no scope of putting more flags?
Solution : When running in the same direction : If the ratio of speeds of two athletes (in the most reducible form) is a : b, the number of distinct meeting points on the track would be would be |a – b|
A and B will meet at |1 - 2| = 1 point.A and C will meet at |1 - 3| = 2 pointsA and D will meet at |1 - 4| = 3 pointsA and E will meet at |1 - 5| = 4 pointsA and F will meet at |1 - 6| = 5 pointsA and G will meet at |1 - 7| = 6 pointsSo A will put 1 + 2 + 3 + 4 + 5 + 6 = 21 flags.
similarly B and C will meet at |2 - 3| = 1 pointB and D will meet at |2 - 4| = 2 pointsB and E will meet at |2 - 5| = 3 pointsB and F will meet at |2 - 6| = 4 pointsB and G will meet at |2 - 7| = 5 pointsSo B will put 1 + 2 + 3 + 4 + 5 = 15 flags
Similarly find for C, D, E and F.
We will get 21 + 15 + 10 + 6 + 3 + 1 = 56 flags

@sumit-agarwal
In such scenarios like finding distinct values of [x^2/n] where x can be from 1, 2, 3 ... n[1^2/n], [2^2/n] ... [(n/2)^2/n] will yield all numbers from 0 to [n/4] (means [n/4] + 1 distinct integers)Then the next set (from [(n/2 + 1)^2/n] till [n^2/n] will be all different integers (means [n/2] distinct integers)So the number of distinct integers would be [n/2] + [n/4] + 1
if n = 100,number of distinct integers would be [100/2] + [100/4] + 1 = 76
if n = 2014,number of distinct integers would be [2014/2] + [2014/4] + 1 = 1511
if n = 13number of distinct integers would be [13/2] + [13/4] + 1 = 10
Just trying to generalize a solution shared by Kamal sir (Quant Boosters - Set 1 - Q2).
You can try out with various numbers (may be smaller numbers) so that this can be verified.

Q97) The percentage profit earned by selling an article at Rs. 1,920 is equal to the percentage loss incurred by selling the same article at Rs. 1,280. At what price (in Rs.) should the article be sold to make a profit of 25%?
[OA: 2000]