The speed of car A is thrice that of car B whereas the speed of car C is twice that of car A. there are three points P, Q and R along a straight line such that point Q is between point P and R. Car starts from Q moving towards R, can A start at P towards R whereas car B starts at point R moving towards P with all the three cars starting simultaneously. The moment car C meets car B, it turns back and start moving towards point Q, such that both car A and car C arrive at point Q simultaneously. If the distance between points P and R is 5200 m, how far (in m) is point Q from point R?

Let speed of B be v. Speed of A = 3v. Speed of C = 6v. Distance PR = 5200. Let Q be at distance x from R. P is at 5200 from R. Car A starts at P (0) towards R (5200). Car B starts at R (5200) towards P (0). Car C starts at Q (5200-x) towards R (5200). Car C meets B at time t1. Distance covered by B = v*t1. Distance covered by C = 6v*t1. C is at Q, moving towards R. B is at R, moving towards P. They meet at distance d from R. d = v*t1 = 6v*t1? No, they move towards each other. Distance between them is x. Time to meet t1 = x / (v+6v) = x/7v. Meeting point from R = v * (x/7v) = x/7. C turns back at x/7 from R. C is now at x/7 from R, moving towards Q. Distance to Q = x - x/7 = 6x/7. Time taken = (6x/7) / 6v = x/7v. Total time for C = x/7v + x/7v = 2x/7v. Car A moves from P to Q. Distance = 5200-x. Time = (5200-x) / 3v. 2x/7v = (5200-x) / 3v. 6x = 36400 - 7x. 13x = 36400. x = 2800.