q: 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) 6/19
(B) 6/11
(C) 6/12
(D) 6/10
(E) 6/38
a: 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 The answer is (B).
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q: A train 260 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
(A) 40 sec
(B) 50 sec
(C) 32 sec
(D) 49 sec
(E) 60 sec
a: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 260 + 140 = 400 m
Required time = 400 * 2/25 = 32 se The answer is (C).
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q: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
(A) 2 kmph.
(B) 4 kmph.
(C) 5 kmph.
(D) 8 kmph.
(E) 7 kmph.
a: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph The answer is (D).
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q: If P(A) = 8/15, P(B) = 4/15, and P(A âˆª B) = 16/15 Find P(B|A)
Options:
(A) 1/2
(B) 2/3
(C) 3/2
(D) 2
(E) 4/7
a:

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
P(B|A) = P(A âˆª B)/P(A)
P(B|A) = (16/15)/(8/15) = 2. The answer is (D).
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