Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
Options:
(A) 5/11
(B) 6/11
(C) 7/11
(D) 8/11
(E) 9/11

Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
Required ratio = 3/10 * 20/11 = 6/11 So the answer is: (B).

A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 410 m long?
Options:
(A) 33 Seconds
(B) 22 Seconds
(C) 41 Seconds
(D) 24 Seconds
(E) 29 Seconds

Distance travelled = 140 + 410m = 550m
Speed = 60 * 5/8 = 50/3m
Time = 550 * 3/50 = 33 Seconds So the answer is: (A).

The speed of a boat in still water is 70kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
(A) 22 kmph
(B) 40 kmph
(C) 78 kmph
(D) 50 kmph
(E) 23 kmph

Speed downstream = 70 + 20 = 90 kmph
Speed upstream = 70 - 20 = 50 kmph So the answer is: (D).

10 people meet and shake hands. The maximum number of handshakes possible if there is to be no “cycle” of handshakes is (A cycle of handshakes is a sequence of k people a1, a2, ……, ak (k > 2) such that the pairs {a1, a2}, {a2, a3}, ……, {ak-1, ak}, {ak, a1} shake hands).
Options:
(A) 7
(B) 6
(C) 9
(D) 8
(E) 10

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
The question is not written in proper manner but we can work in 3 methods
1) If these are random handshakes, then total methods = 10*9/2*1 = 45
2) If these are cyclic handshakes, then total methods = 10
3) If these persons are not cyclic but they are arranged in a straight bench, then number of methods = 9 So the answer is: (C).