11. Pipes and cisterns
Free study material · concepts, shortcuts & solved questions
Treat filling pipes as positive rates and emptying pipes as negative rates. If an inlet fills in x hours, its rate is 1/x; a leak emptying in y hours has rate −1/y. Net time is 1 ÷ net rate.
Method before formula A pipe may be open only for part of the time. Split the timeline into intervals and subtract the work already done before changing the rate. |
Formula and decision table
Example | Calculation |
Inlet 6 h, leak 12 h | Net=1/6−1/12=1/12; fill in 12 h |
Two inlets | Rates add |
Drain opened later | Work before and after drain separately |
Worked understanding
A reliable solution has five visible moves: identify the data, choose the base or unit, write the rule, substitute carefully, and check the size of the answer. The examples in this chapter are deliberately small so that the method remains visible.
Calculation discipline Before pressing ahead, state the denominator or unit in words. For example: profit on CP, discount on MP, average over number of items, speed in metres per second, and probability over the fixed sample space. |
Solved examples from this chapter
Question focus | Correct move | Answer |
Inlet fills in 6 h, leak empties in 12 h. Net time: | Net rate is 1/12 tank per hour. | C. 12 h |
An outlet is represented by a: | It removes water. | B. Negative rate |
Two inlets fill in 10 h and 15 h. Together time: | Rate=1/10+1/15=1/6. | B. 6 h |
What an examiner is testing
The options around Pipes and cisterns usually represent a wrong base, a missed conversion, a sign error or a shortcut used outside its condition. Say the base and unit before calculating, estimate the result, and use substitution or a reverse operation as the final check.
Step-by-step answer construction
Example 1: Inlet fills in 6 h, leak empties in 12 h. Net time: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 12 h, because Net rate is 1/12 tank per hour.
Example 2: An outlet is represented by a: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is Negative rate, because It removes water.
Example 3: Two inlets fill in 10 h and 15 h. Together time: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 6 h, because Rate=1/10+1/15=1/6.
Chapter practice
1. Inlet fills in 6 h, leak empties in 12 h. Net time:
(A) 6 h (B) 8 h (C) 12 h (D) 18 h
Answer: C. 12 h | Explanation: Net rate is 1/12 tank per hour.
2. An outlet is represented by a:
(A) Positive rate (B) Negative rate (C) Zero rate always (D) Percentage
Answer: B. Negative rate | Explanation: It removes water.
3. Two inlets fill in 10 h and 15 h. Together time:
(A) 5 h (B) 6 h (C) 7.5 h (D) 25 h
Answer: B. 6 h | Explanation: Rate=1/10+1/15=1/6.
SSC CGL speed and trap clinic
For Pipes and cisterns, speed comes after classification. Before calculating, say aloud what the number means, what the denominator is, and what unit the answer must carry. Then use the nearest-option check to catch a sign, base or conversion error.
Checkpoint | What to verify | Typical SSC mistake |
Base | Which quantity is the base in Pipes and cisterns? | Using selling price instead of cost price, or part instead of total |
Unit | Are time, distance, area and rate in compatible units? | Mixing hours with minutes or km/h with m/s |
Direction | Should the answer increase, decrease or stay bounded? | Accepting an impossible negative length or probability above 1 |
Estimate | What range should the answer lie in before exact work? | Trusting a long calculation that is far from the options |
Reverse check | Can the answer be substituted back into the condition? | Stopping at an algebraic value without verification |
Mini decision drill
1. Write the first operation you would perform in a Pipes and cisterns question and why.
2. State the most dangerous denominator or unit in this chapter.
3. Give one condition under which a shortcut would be invalid.
4. Create a small numerical example and verify it by a second method.
Revision evidence Do not tick this chapter because you recognised the formula. Tick it only after you solve one direct question, one altered-condition question and one mixed-paper question correctly. |