Pipes and Cisterns
5 solved SSC CGL Quantitative Aptitude previous year questions on Pipes and Cisterns, each with the correct answer and a full explanation.
Q1
There are two water taps in a tank which can fill the empty tank in 12 hours and 18 hours respectively. It is seen that there is a leakage point at the bottom of the tank which can empty the completely filled tank in 36 hours. If both the water taps are opened at the same time to fill the empty tank and the leakage point was repaired after 1 hour, then in how much time the empty tank will be completely filled?
✓ Correct answer: c) 7 hours 24 minutes
ExplanationLet the capacity of the tank be 36a litres.Then, efficiency of tap 1 = 36a/12 = 3a litres/hour, Efficiency of tap 2 = 36a/18 = 2a litres/hour And efficiency of leakage point = -36a/36 = -a litres/hour Combined efficiency of all taps = 3a + 2a = 5a litres/hours Capacity filled in first hour = 5a – a = 4a litres Remaining capacity = 36a – 4a = 32a litres Time taken to fill the remaining capacity = 32a/5a = 6.4 hours Total time taken = 1 + 6.4 = 7.4 hours = 7 hours 24 minutes Hence, Option C is the correct answer.
Q2
Pipe A can fill a tank in 12 minutes; pipe B can fill it in 18 minutes, while pipe can empty the full tank in 36 minutes. If all the pipes are opened simultaneously, how much time will it take to fill the empty tank completely?
✓ Correct answer: c) 9 minutes
ExplanationPipe A can fill the tank = 12 min Pipe B can fill the tank = 18 min Pipe C can empty the tank = 36 min According to question, Part of tank filled by all three pipes in 1 min Time taken = 9 min Hence, the correct answer is (C).
Q3
Each inlet pipe can fill an empty cistern in 84 hours while each drain pipe can empty the same cistern from a filled condition in 105 hours. When the cistern is empty, 9 inlet pipes and 10 outlet pipes are simultaneously opened. After how many hours will the cistern be completely filled?
✓ Correct answer: a) 84
ExplanationEach inlet pipe can fill an empty cistern in 84 hours while each drain pipe can empty the same cistern from a filled condition in 105 hours LCM of 84, 105 = 420 Let the total capacity of cistern be 420 unit.Total capacity = Efficiency Time taken Efficiency of each inlet pipe = = 5 unit/hr Efficiency of each outlet pipe = = 4 unit/hr When the cistern is empty, 9 inlet pipes and 10 outlet pipes are simultaneously opened.Efficiency of 9 inlet pipe = 5 9 = 45 unit/hr Efficiency of 10 outlet pipe = 4 10 = 40 unit/hr the cistern will be completely filled = = = 84 hours So,correct option is A.
Q4
A pipe can fill a tank in 30 hours. Due to a leakage at the bottom, it is filled in 50 hours. How much time will the leakage take to empty the completely filled tank?
✓ Correct answer: d) 75 hours
ExplanationLet the leakage can empty the completely filled tank in x hours.Part filled by the pipe in 1 hour = Part filled by the pipe and leakage in 1 hour = = = x = 75 So, the leakage will take 75 hours to empty the filled tank.Hence, Option D is correct
Q5
Pipe A can fill of the tank in 6 hours and pipe B can completely fill the same tank in 18 hours. If both the pipes are opened at the same time, in how much time (in minutes) will the empty tank be completely filled?
✓ Correct answer: c) 432
ExplanationTime taken by pipe A fill the 50% of tank = 6hrs Time taken by pipe A fill the 100% of tank = 6 2 = 12hrs Time taken by pipe B fill the tank = 18 hrs Now, Portion of tank filled by both pipes together in 1 hour, So, time taken to fill the tank when both the pipes are opened together = hrs = minutes Hence, Option C is the correct answer.
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