Pipes & Cisterns Questions with Solutions

Pipes and cisterns questions are an application of time and work. An inlet pipe fills a tank and does positive work, while an outlet pipe or leak empties it and does negative work. If an inlet pipe fills a tank in a hours, it fills 1/a of the tank each hour. If an outlet pipe empties it in b hours, it removes 1/b each hour. Questions involve several pipes opened together, pipes opened or closed partway through, leaks that slow down filling, and pipes with different filling rates. The LCM method works especially well. Take the tank's capacity as the LCM of the given times, find each pipe's rate in units per hour (negative for outlet pipes and leaks), and add the rates. This avoids fractions entirely. Always check whether the question asks for the time to fill or the time to empty. Practise the pipes and cisterns questions below, each with a step-by-step solution using the LCM method.