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1) Two pipes A and B can fill a tank in 24min and 32 min respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 mins?A) 7 B) 9 C) 8 D) 6
Answer & Explanation
Answer: 8 (Let B be closed after x minutes. Then,
Part filled by (A+B) in x min+ part filled by A in (18-x)min=1
x(1/24+1/32)+(18-x)*1/24=1
7x/96+18-x/24=1
7x+4(18-x)=96
x=8. Hence, B must be closed after 8 mins.
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2) Two pipes A and B can fill a tank in 18 hrs and 36 hrs respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?A) 80 B) 9 C) 10 D) 12
Answer & Explanation
Answer: 12 (Part filled by A in 1hr= 1/18. Part filled by B in 1hr= 1/36
Part filled by (A+B) in 1hr= (1/18+1/36) = 15/180 =1/12
Hence, both the pipes together will fill tank in 12hrs.
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3) Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 6 minutes, pipe A is turned off. What is the total time required to fill the tank?A) 13 B) 12 C) 15 D) 10
Answer & Explanation
Answer: 12 (Part filled in 6 minutes = 6* (1/15 + 1/20) = 7/10
Remaining part = 1 - 7/10 = 3/10
Part filled by B in 1 minute = 1/20
1/20 : 3/10 :: 1 : x
x = (3/10) x 1 x 20 = 6 min
The tank will be full in (6 min. + 6 min.) = 12 min.
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4) Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in:A) 8 B) 5 C) 7 D) 6
Answer & Explanation
Answer: 7 ((A + B)'s fills = 1/12 + 1/15 = 9/60 = 3/20 . (A + C)'s fills = 1/12 + 1/20 = 8/60 = 2/15 .
Part filled in 2 hrs = 3/20 + 2 /15 = 17/60 .
Part filled in 6 hrs = 3 x 17/60 = 17/20 .
Remaining part = 1 - 17/20 = 3/20 .
Now, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.
Total time taken to fill the tank = (6 + 1) hrs = 7 hrs.
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5) A cistern is filled by pipe A in 12hrs and the full cistern can be leaked out by an exhaust pipe B in 15hrs. If both the pipes are opened, in what time the cistern is full?A) 65 B) 50 C) 40 D) 60
Answer & Explanation
Answer: 60 (Work done by the inlet in 1 hr = 1/12
Work done by the outlet in 1 hr = 1/15
Net part filled in 1 hr=(1/12-1/15) = 1/60
Therefore,the cistern will be full in 60hrs.
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