# Pipes and Cisterns

- The problems of pipes and cisterns usually have two kinds of pipes, Inlet pipe and Outlet pipe / Leak. Inlet pipe is the pipe that fills the tank/reservoir/cistern and Outlet pipe / Leak is the one that empties it.
- If a pipe can fill a tank in ‘n’ hours, then in 1 hour, it will fill ‘1 / n’ parts. For example, if a pipe takes 6 hours to fill a tank completely, say of 12 liters, then in 1 hour, it will fill 1 / 6 th of the tank, i.e., 2 liters … More on Pipes and CisternsQuestion 1Two outlet pipes A and B are connected to a full tank. Pipe A alone can empty the tank in 10 minutes and pipe B alone can empty the tank in 30 minutes. If both are opened together, how much time will it take to empty the tank completely?7 minutes7 minutes 30 seconds6 minutes6 minutes 3 seconds
**Pipes and Cisterns****Discuss it**Question 1 Explanation:Let the capacity of the tank be LCM(10, 30) = 30 units. => Efficiency of pipe A = 30 / 10 = 3 units / minute => Efficiency of pipe A = 30 / 30 = 1 units / minute => Combined efficiency of pipe A and pipe B = 4 units / minute Therefore, time required to empty the tank if both pipes work = 30 / 4 = 7 minutes 30 secondsQuestion 2Two pipes A and B attached to a swimming pool can fill the pool in 20 minutes and 30 minutes respectively working alone. Both were opened together but due to malfunctioning of motor of pipe A, it had to be shut down after two minutes but B continued to work till the swimming pool was filled completely. Find the total time taken to fill the pool.20222527**Pipes and Cisterns****Discuss it**Question 2 Explanation:Let the capacity of the pool be LCM(20, 30) = 60 units. => Efficiency of pipe A = 60 / 20 = 3 units / minute => Efficiency of pipe B = 60 / 30 = 2 units / minute => Combined efficiency of pipe A and pipe B = 5 units / minute Now, the pool is filled with the efficiency of 5 units / minute for two minutes. => Pool filled in two minutes = 10 units => Pool still empty = 60 - 10 = 50 units This 50 units is filled by B alone. => Time required to fill these 50 units = 50 / 2 = 25 minutes Therefore, total time required to fill the pool = 2 + 25 = 27 minutesQuestion 3Three pipes A, B and C were opened to fill a cistern. Working alone, A, B and C require 12, 15 and 20 minutes respectively.After 4 minutes of working together, A got blocked and after another 1 minute, B also got blocked. C continued to work till the end and the cistern got completely filled. What is the total time taken to fill the cistern ?6 minutes6 minutes 15 seconds6 minutes 40 seconds6 minutes 50 seconds**Pipes and Cisterns****Discuss it**Question 3 Explanation:Let the capacity of the cistern be LCM(12, 15, 20) = 60 units. => Efficiency of pipe A = 60 / 12 = 5 units / minute => Efficiency of pipe B = 60 / 15 = 4 units / minute => Efficiency of pipe C = 60 / 20 = 3 units / minute => Combined efficiency of pipe A, pipe B and pipe C = 12 units / minute Now, the cistern is filled with the efficiency of 12 units / minute for 4 minutes. => Pool filled in 4 minutes = 48 units => Pool still empty = 60 – 48 = 12 units Now, A stops working. => Combined efficiency of pipe B and pipe C = 7 units / minute Now, the cistern is filled with the efficiency of 7 units / minute for 1 minute. => Pool filled in 1 minute = 7 units => Pool still empty = 12 – 7 = 5 units Now, B also stops working. These remaining 5 units are filled by C alone. => Time required to fill these 5 units = 5 / 3 = 1 minute 40 seconds Therefore, total time required to fill the pool = 4 minutes + 1 minutes + 1 minute 40 seconds = 6 minutes 40 secondsQuestion 4Three pipes A, B and C are connected to a tank. Working alone, they require 10 hours, 20 hours and 30 hours respectively. After some time, A is closed and after another 2 hours, B is also closed. C works for another 14 hours so that the tank gets filled completely. Find the time (in hours) after which pipe A was closed.11.523**Pipes and Cisterns****Discuss it**Question 4 Explanation:Let the capacity of the tank be LCM (10, 20, 30) = 60 => Efficiency of pipe A = 60 / 10 = 6 units / hour => Efficiency of pipe B = 60 / 20 = 3 units / hour => Efficiency of pipe C = 60 / 30 = 2 units / hour Now, all three work for some time, say 't' hours. So, B and C work for 2 more hours after 't' hours and then, C works for another 14 hours. => Combined efficiency of pipe A, pipe B and pipe C = 11 units / hour => Combined efficiency of pipe B and pipe C = 5 units / hour So, we have 11 x t + 5 x 2 + 14 x 2 = 60 => 11 t + 10 + 28 = 60 => 11 t = 60 - 38 => 11 t = 22 => t = 2 Therefore, A was closed after 2 hours.Question 5Working alone, two pipes A and B require 9 hours and 6.25 hours more respectively to fill a pool than if they were working together. Find the total time taken to fill the pool if both were working together.66.577.5**Pipes and Cisterns****Discuss it**Question 5 Explanation:Let the time taken if both were working together be 'n' hours. => Time taken by A = n + 9 => Time taken by B = n + 6.25 In such kind of problems, we apply the formula : n^{2}= a x b, where 'a' and 'b' are the extra time taken if both work individually than if both work together. Therefore, n^{2}= 9 x 6.25 => n = 3 x 2.5 = 7.5 Thus, working together, pipes A and B require 7.5 hours.Question 6Three pipes A, B and C were opened to fill a cistern. Working alone, A, B and C require 12, 15 and 20 minutes respectively. Another pipe D, which is a waste pipe, can empty the filled tank in 30 minutes working alone. What is the total time (in minutes) taken to fill the cistern if all the pipes are simultaneously opened ?5678**Pipes and Cisterns****Discuss it**Question 6 Explanation:Let the capacity of the cistern be LCM(12, 15, 20, 30) = 60 units. => Efficiency of pipe A = 60 / 12 = 5 units / minute => Efficiency of pipe B = 60 / 15 = 4 units / minute => Efficiency of pipe C = 60 / 20 = 3 units / minute => Efficiency of pipe D = 60 / 30 = 2 units / minute => Combined efficiency of pipe A, pipe B, pipe C and pipe D = 10 units / minute Therefore, time required to fill the cistern if all the pipes are opened simultaneously = 60 / 10 = 6 minutesQuestion 7Three pipes A, B and C were opened to fill a tank. Working alone, A, B and C require 10, 15 and 20 hours respectively. A was opened at 7 AM, B at 8 AM and C at 9 AM. At what time the tank would be completely filled, given that pipe C can only work for 3 hours at a stretch, and needs 1 hour standing time to work again.12 : 00 PM12 : 30 PM1 : 30 PM1 : 00 PM**Pipes and Cisterns****Discuss it**Question 7 Explanation:Let the capacity of the tank be LCM (10, 15, 20) = 60 => Efficiency of pipe A = 60 / 10 = 6 units / hour => Efficiency of pipe B = 60 / 15 = 4 units / hour => Efficiency of pipe C = 60 / 20 = 3 units / hour => Combined efficiency of all three pipes = 13 units / hour Till 9 AM, A works for 2 hours and B work for 1 hour. => Tank filled in 2 hours by A = 12 units => Tank filled in 1 hour by B = 4 units => Tank filled till 9 AM = 16 units => Tank still empty = 60 - 16 = 44 units Now, all three pipes work for 3 hours with the efficiency of 13 units / hour. => Tank filled in 3 more hours = 39 units => Tank filled till 12 PM = 16 + 39 units = 55 units => Tank empty = 60 - 55 = 5 units Now, C is closed for 1 hour and these remaining 5 units would be filled by A and B working together with the efficiency 10 units / hour. => Time taken to fill these remaining 5 units = 5 / 10 = 0.5 hours Therefore, time at which the tank will be completely filled = 12 PM + 0.5 hours = 12 : 30 PMQuestion 8Two pipes A and B can fill a tank in 10 hours and 30 hours respectively. Due to a leak in the tank, it takes 2.5 hours more to fill the tank. How much time would the leak alone will take to empty the tank ?20 hours25 hours30 hours35 hours**Pipes and Cisterns****Discuss it**Question 8 Explanation:Let the capacity of the tank be LCM (10, 30) = 30 units => Efficiency of pipe A = 30 / 10 = 3 units / hour => Efficiency of pipe B = 30 / 30 = 1 units / hour => Combined efficiency of both pipes = 4 units / hour Now, total time taken by A and B working together to fill the tank if there was no leak = 30 / 4 = 7.5 hours => Actual time taken = 7.5 + 2.5 = 10 hours The tank filled by A and B in these 2.5 hours is the extra work done to compensate the wastage by the leak in 10 hours. => 2.5 hours work of A and B together = 10 hours work of the leak => 2.5 x 4 = 10 x E, where 'E' is the efficiency of the leak. => E = 1 unit / hour Therefore, time taken by the leak alone to empty the full tank = 30 / 1 = 30 hoursQuestion 9Two pipes A and B work alternatively with a third pipe C to fill a swimming pool. Working alone, A, B and C require 10, 20 and 15 hours respectively. Find the total time required to fill the pool.7 hours 14 minutes6 hours 54 minutes5 hours 14 minutes8 hours 54 minutes**Pipes and Cisterns****Discuss it**Question 9 Explanation:Let the capacity of the pool be LCM (10, 20, 15) = 60 units. => Efficiency of pipe A = 60 / 10 = 6 units / hour => Efficiency of pipe B = 60 / 20 = 3 units / hour => Efficiency of pipe C = 60 / 15 = 4 units / hour => Efficiency of pipe A and pipe C working together = 10 units / hour => Efficiency of pipe B and pipe C working together = 7 units / hour => Pool filled in first hour = 10 units => Pool filled in second hour = 7 units => Pool filled in 2 hours = 10 + 7 = 17 units We will have 3 cycles of 2 hours each such that A and C, and, B and C work alternatively. => Pool filled in 6 hours = 17 x 3 = 51 units => Pool empty = 60 - 51 = 9 units Now, these 9 units would be filled by A and C working together with the efficiency of 10 units / hour. => Time required to fill these 9 units = 9/10 hour = 0.9 hours = 54 minutes Therefore, total time required to fill the pool = 6 hours 54 minutesQuestion 10Two pipes A and B are connected to drain out a water tank. A alone can drain out the tank in 20 hours and B can drain 20 liters per hour. Find the capacity of the water tank given that working together, they require 12 hours to completely drain out the tank.600400800700**Pipes and Cisterns****Discuss it**Question 10 Explanation:Let the capacity of the tank be LCM (20, 12) = 60 units => Efficiency of A working alone = 60 / 20 = 3 units / hour => Efficiency of A and B working together = 60 / 12 = 5 units / hour Therefore, Efficiency of B working alone = Efficiency of A and B working together - Efficiency of A working alone => Efficiency of B working alone = 5 - 3 = 2 units / hour => Time required by B alone to drain the tank = 60 / 2 = 30 hours But we are given that B can drain the tank at the rate of 20 liters per hour. Therefore, capacity of the water tank = 20 x 30 = 600 litersThere are 15 questions to complete.