q: A man started running at a distance of 225 metre from the train. If the speed of the man is 6 km/h, then how much time should the train wait so that the man will be just able to catch it ?
Options:
(A) 2 1⁄4 min
(B) 3 min
(C) 4 1⁄4 min
(D) 4 1⁄2 min
(E) None of these
a: Time = 225/6×518 = 135 sec = 21⁄4 min. The answer is (A).
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q: A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 45 minutes. When both pipes are opened, find when the cistern will be full?
Options:
(A) 17 minutes
(B) 87 minutes
(C) 36 minutes
(D) 27 minutes
(E) 11 minutes
a: 1/20 - 1/45 = 1/36
36 minutes The answer is (C).
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q: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Options:
(A) 25200
(B) 2543
(C) 2344
(D) 233445
(E) 52757
a: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) = (7C3 x 4C2) = ( 7 x 6 x 5 x 4 x 3 ) 3 x 2 x 1 2 x 1 = 210. Number of groups, each having 3 consonants and 2 vowels = 210. Each group contains 5 letters. Number of ways of arranging 5 letters among themselves = 5! = 5 x 4 x 3 x 2 x 1 = 120. Required number of ways = (210 x 120) = 25200. The answer is (A).
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q: A man rows his boat 90 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
(A) 5 kmph
(B) 7 kmph
(C) 9 kmph
(D) 8 kmph
(E) 1 kmph
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
Speed downstream = d/t = 90/(2 1/2) = 36 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (36 - 18)/2 = 9 kmph The answer is (C).
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