Pipes and cisterns

Story hook

It is a hot summer morning. The big black water tank on your rooftop is completely empty, and you want a bath. So you open the tap that lets water flow into the tank.

You watch and time it. The tap fills the whole tank in exactly 2 hours when it runs all by itself.

Now here is the fun part. While that tap is busy filling, there is a small hole at the bottom of the tank that has been leaking for weeks. On its own, that leak would empty a full tank in 6 hours.

So one thing is pouring water in, and another thing is draining water out — both at the same time. A natural question pops up: with the tap on and the leak open together, how long will the tank take to fill?

That little tug-of-war between water coming in and water going out is the whole story of pipes and cisterns. A "cistern" is just a fancy word for a water tank. By the end of this lesson you will solve that rooftop puzzle in your head. Let's start from absolute zero.

Why this matters for UPSC

For your CSAT exam (UPSC Prelims Paper II):

• CSAT is a qualifying paper — you do not need a sky-high score, you just need 33% (that is 66 marks out of 200) to clear it. Pipes and cisterns is one of the most predictable, formula-friendly topics. Once you learn one simple idea, almost every question falls open.
• Good news: it is really the same maths as "time and work" dressed up with water taps. A filling pipe is just a "worker" who does positive work; a draining pipe is a "worker" who undoes work. Learn it once, use it twice.

For real life (this is the useful part):

• You will know how long your overhead tank takes to fill in the morning so you can plan your bath and not run dry.
• You will understand a leaking drum or bucket — how a slow drip steals your stored water over a day.
• You will be able to reason about a bathtub with the tap running and the plug slightly open — should you bother, or will it never fill?
• It trains a calm habit: add what helps, subtract what hurts, and see what is left. That clear thinking is useful far beyond water tanks.

So relax — this is a friendly topic built on one neat idea: work out how much gets done in one hour. Follow along slowly and it will click.