Pipes and Cisterns, Boats and Streams Notes for Competitive Exams

Pipes and cisterns and boats and streams are two popular chapters in the quantitative aptitude section of SSC, banking, railways, defence and state-level examinations. The questions look different, but they use the same idea as time and work and time, speed and distance: find the rate of each part, add or subtract the rates, and then find the time. A student who learns a few formulas and practises the standard types can solve these questions in less than a minute. This note explains both chapters with formulas, solved examples, tricks and practice questions, in simple language.

Part 1: Pipes and Cisterns

A pipe connected to a tank (cistern) is of two kinds. An inlet pipe fills the tank, and an outlet pipe (or leak) empties it. The idea is the same as in the work and time chapter: the filling of the whole tank is one unit of work. If an inlet fills the tank in x hours, its work in one hour is 1/x of the tank. If an outlet empties the tank in y hours, its work in one hour is -1/y (negative, because it removes the water).

Basic Formulas

Solved Examples on Pipes and Cisterns

1. Pipe A fills a tank in 6 hours and pipe B in 12 hours. In how many hours will they fill it together? Time = (6 x 12) / (6 + 12) = 72 / 18 = 4 hours.
2. An inlet fills a tank in 4 hours, and an outlet empties it in 6 hours. If both are open, in how many hours will the tank fill? Net rate = 1/4 - 1/6 = 1/12 per hour, so the time is 12 hours.
3. A tank is filled in 6 hours by a pipe, but because of a leak, it takes 8 hours. In how many hours will the leak empty the full tank? Leak rate = 1/6 - 1/8 = 1/24, so the leak will empty the tank in 24 hours.
4. Pipes A and B can fill a tank in 10 and 15 hours, and pipe C can empty it in 20 hours. If all are opened together, how long will it take to fill the tank? Net rate = 1/10 + 1/15 - 1/20 = (6 + 4 - 3) / 60 = 7/60, so the time = 60/7 = 8 4/7 hours.
5. Pipes A (6 hours) and B (12 hours) are opened alternately for one hour each, starting with A. When will the tank be full? In 2 hours, the work is 1/6 + 1/12 = 1/4. So 8 hours will fill the tank, and the answer is 8 hours.

Tricks for Pipes and Cisterns

• Take the LCM of the times as the capacity of the tank, and find the litres per hour of each pipe. This makes the arithmetic easy.
• If the tank is partly filled before a pipe is opened, subtract that part first.
• For the alternate-opening questions, find the work done in one full cycle first, and then the remaining part.
• Always note which pipe is inlet (positive) and which is outlet (negative).

Part 2: Boats and Streams

When a boat moves in a river, the speed of the water (the stream) helps it when it moves with the current and slows it when it moves against it. Let the speed of the boat in still water be u and the speed of the stream be v (both in km per hour).

Remember that the downstream speed is always more than the upstream speed, and the stream speed is always less than the boat's speed, otherwise the boat cannot go upstream. The same formulas apply to a swimmer or an aeroplane flying with or against the wind.

Solved Examples on Boats and Streams

1. A boat goes at 15 km/h in still water, and the stream runs at 3 km/h. Find the downstream and upstream speeds. Downstream = 15 + 3 = 18 km/h; upstream = 15 - 3 = 12 km/h.
2. The downstream speed of a boat is 20 km/h, and the upstream speed is 12 km/h. Find the speed in still water and the speed of the stream. u = (20 + 12) / 2 = 16 km/h; v = (20 - 12) / 2 = 4 km/h.
3. A boat takes 2 hours to go 36 km downstream and how much time to return if the upstream speed is 12 km/h? Time upstream = 36 / 12 = 3 hours.
4. A man can row at 6 km/h in still water, and the river flows at 2 km/h. He goes to a place and comes back in a total of 6 hours. How far is the place? Downstream speed = 8, upstream = 4. Let the distance be d: d/8 + d/4 = 6, so 3d/8 = 6, and d = 16 km.
5. The time taken to row a certain distance upstream is twice the time downstream. Find the ratio of the boat's speed to the stream's speed. The speeds are in the ratio 1:2 for upstream and downstream, so (u - v) : (u + v) = 1 : 2. This gives u = 3v, so the ratio is 3 : 1.

Tricks for Boats and Streams

• Write the downstream and upstream speeds first, and then find u and v with the average and half the difference.
• If the question gives the ratio of the times for the same distance, take the inverse for the ratio of the speeds.
• For a round trip, use the average-speed formula 2DU/(D + U) and not the simple average of the two speeds.
• Convert the units of speed and time (km/h and minutes) before you start.

Common Mistakes

In the pipes and cisterns, students often forget to subtract the rate of the outlet, or mix the time to fill with the rate per hour. In the boats and streams, they confuse upstream with downstream or take the simple average for a round-trip speed. Another common error is to apply the formula without checking that the stream speed is less than the speed of the boat. Read each question twice and write the data in a small table.

Practice Questions With Answers

• Q1. Two pipes fill a tank in 20 and 30 hours. In how many hours will both fill it together? Answer: 12 hours.
• Q2. A pipe fills a tank in 5 hours, and a leak empties the full tank in 10 hours. In how many hours will it fill with the leak? Answer: 10 hours.
• Q3. A boat goes 24 km downstream in 2 hours and returns in 3 hours. Find the speed of the boat in still water. Answer: 10 km/h (downstream 12, upstream 8).
• Q4. The speed of a boat in still water is 9 km/h, and the stream is 1 km/h. How long to go 40 km downstream? Answer: 4 hours.

Revise the related chapters of time and work and time, speed and distance.

Memory Tip

For pipes, remember "inlet adds, outlet subtracts"; for boats, remember "down is plus, up is minus". With these two short lines and the LCM method, most questions of these chapters can be solved quickly in the examination hall.

Quick Revision

• Pipes: inlet is +1/x; outlet is -1/y; two inlets together = ab/(a + b).
• Boats: downstream = u + v; upstream = u - v; u = (D + U)/2; v = (D - U)/2.
• Use the LCM of the times as the capacity to simplify the pipe problems.

Frequently Asked Questions (FAQ)

What is an inlet pipe in a tank problem?

An inlet pipe is a pipe that fills the tank, and its work per hour is counted as positive.

What is an outlet pipe?

An outlet pipe empties the tank, and its work per hour is counted as negative.

How do I find the time taken by two pipes together to fill a tank?

If they take a and b hours alone, the time together is (a x b) / (a + b).

How do I find the time to fill when an inlet and an outlet are open?

Subtract the rates: net rate = 1/x - 1/y, and the time is the reciprocal of this rate.

How do I find the time for a leak to empty a tank?

Subtract the rate of filling with the leak from the normal rate of filling, and take the reciprocal.

What is the downstream speed?

Downstream speed is the speed of the boat in still water plus the speed of the stream.

What is the upstream speed?

Upstream speed is the speed of the boat in still water minus the speed of the stream.

How do I find the speed of the boat in still water?

It is half the sum of the downstream and the upstream speeds.

How do I find the speed of the stream?

It is half the difference of the downstream and the upstream speeds.

How do I find the average speed of a round trip?

Use 2DU / (D + U), where D and U are the downstream and the upstream speeds.

Why must the stream speed be less than the boat speed?

If the stream speed is more, the boat cannot move upstream.

Which chapters are related to pipes and cisterns?

Time and work is the closest, and the same method of rates is used.