Time and Work Pipes Cisterns Questions for UP POLICE CONSTABLE

Core Concept: Work Rate and Efficiency

In pipes and cisterns, we treat each pipe as a 'worker' with a specific work rate. If a pipe fills a tank in 10 hours, its rate is 1/10 of the tank per hour. If a pipe empties a tank in 15 hours, its rate is -1/15 per hour (negative because it removes water). When pipes work together, their rates add up algebraically. The key insight: always think in terms of 'fraction of tank per unit time', not absolute volumes.

• Inlet pipe (fills tank): positive work rate = 1/time taken
• Outlet pipe (empties tank): negative work rate = -1/time taken
• Combined rate = sum of individual rates (with signs)
• Time to complete combined work = 1 / combined rate
• If combined rate is negative, the tank empties; if positive, it fills

Two-Pipe Problems: Standard Pattern

Most UP Police papers ask: 'Pipe A fills a tank in 6 hours, Pipe B empties it in 9 hours. How long to fill if both open?' This is a classic combined-rate problem. Calculate individual rates, add them (with correct signs), then invert to get time. Watch the wording carefully: 'fills' = positive, 'empties' = negative.

• Identify which pipes fill (positive) and which empty (negative)
• Write rate for each: Rate_A = 1/6, Rate_B = -1/9
• Combined rate = 1/6 - 1/9 (find common denominator)
• Time = 1 / combined rate
• Always check: does answer make sense? (Should be between slowest and fastest individual time)

Three-Pipe and Partial-Opening Problems

Harder variants involve 3 pipes or pipes opening/closing at different times. For 3 pipes: calculate all three rates, sum them. For partial opening: calculate combined rate for the first period, then adjust when a pipe closes/opens, and recalculate. Break the problem into time intervals and track cumulative work.

• Three pipes: R_total = R_A + R_B + R_C (with signs)
• Partial opening: split into phases, calculate work in each phase separately
• Track cumulative work: if 1/4 tank filled in phase 1, remaining = 3/4 for phase 2
• Recalculate time for remaining work using new combined rate
• Common trap: forgetting to subtract work already done before calculating remaining time

Leak and Waste Problems

A 'leak' or 'waste' is an outlet pipe that drains water unintentionally. Treat it exactly like an emptying pipe: negative work rate. If a tank has a leak that empties a full tank in 20 hours, its rate is -1/20. The presence of a leak increases the time to fill the tank.

• Leak = outlet pipe with negative rate
• Combined rate with leak = inlet rate - leak rate
• If leak rate is large, tank may never fill (combined rate ≤ 0)
• Check: if combined rate is negative or zero, answer is 'never fills' or 'infinity'
• Leak problems often ask: 'How long to fill if leak is present vs. absent?'

Inverse Problems: Finding Individual Times

Sometimes the exam gives combined time and asks for individual pipe time. Example: 'Pipes A and B together fill in 6 hours. A alone fills in 10 hours. How long for B alone?' Use algebra: if R_A + R_B = 1/6 and R_A = 1/10, then R_B = 1/6 - 1/10. Solve for T_B.

• Write equation: R_A + R_B = R_combined
• Substitute known rates, solve for unknown
• Be careful with signs: if one empties, use subtraction
• Check: combined time should be less than fastest individual pipe (if both fill)

• Forgetting to use negative sign for outlet/emptying pipes. Many students add all rates as positive and get wrong answer. Always: inlet = +, outlet = -.
• Confusing 'time to fill' with 'rate'. If pipe fills in 10 hours, rate is 1/10, NOT 10. Invert the time.
• Not finding common denominator when adding fractions. 1/6 + 1/9 is NOT 2/15. Find LCM: 1/6 + 1/9 = 3/18 + 2/18 = 5/18.
• In partial-opening problems, forgetting to subtract work already done. If 1/3 tank filled in phase 1, remaining is 2/3, not 1/3.
• Misreading 'both pipes open' vs 'pipes open alternately'. Simultaneous = add rates. Alternating = split time and calculate separately.

• INLET = POSITIVE, OUTLET = NEGATIVE. Think: water in = +, water out = -. Like bank account: deposit is +, withdrawal is -.
• RATE = 1/TIME. Always invert. If fills in 5 hours, rate is 1/5 per hour. If empties in 10 hours, rate is -1/10 per hour.
• COMBINED RATE = SUM OF RATES. Then TIME = 1 / COMBINED. Two-step process: add rates, invert result.
• LCM IS YOUR FRIEND. When adding fractions like 1/6 + 1/9, find LCM(6,9)=18, convert to 3/18 + 2/18 = 5/18. Avoids decimals and errors.

• UP Police typically asks 2-3 pipes and cisterns questions per paper. Usually 1 straightforward two-pipe problem (6-8 min), 1 three-pipe or partial-opening (10-12 min). Difficulty: moderate.
• Watch for 'trick' wording: 'pipe A fills tank in 6 hours' vs 'pipe A fills 1/6 of tank in 1 hour' (same thing, but second form is rate directly). Read carefully.
• Time management: these questions are solvable in 5-8 minutes if you know the method. Don't spend >10 minutes on one question; move on and come back.
• Common wrong options in MCQ: answers that use only one pipe's time, or answers that add times instead of rates. If you see 'sum of times', it's likely wrong.
• Recent papers (2022-2024) show preference for 2-pipe problems with one inlet and one outlet (leak scenario). Practice this pattern heavily.