Time, Work & Pipes/Cisterns

Ditch the classical fraction method (1/x + 1/y). The LCM Unitary method assumes the total work to be the LCM of given days, turning fractions into small whole-number efficiencies.

Exam Frequency: 2 to 4 questions across all IT and Bank recruitment exams

Essential Formulas & Shortcut Rules

Total Work = Time Taken × Worker Efficiency (Units/day)

The fundamental relationship connecting output and rate.

Work Done = (M₁ × D₁ × H₁ × E₁) / W₁ = (M₂ × D₂ × H₂ × E₂) / W₂

Men-Days-Hours formula for group work scaling.

Net Filling Rate = Inlets Rate - Outlets Leak Rate

For pipes and cisterns where leaks drain volume.

Worked Step-by-Step Examples

Example 1: A can complete a project in 20 days and B can finish it in 30 days. They work together for 5 days, after which A leaves due to illness. In how many more days will B finish the remaining work alone?

Step-by-Step Mathematical Derivation:

•Total Work = LCM(20, 30) = 60 units.

•A's rate = 60 / 20 = 3 units/day. B's rate = 60 / 30 = 2 units/day.

•Combined rate (A + B) = 3 + 2 = 5 units/day.

•Work done in first 5 days together = 5 days × 5 units/day = 25 units.

•Remaining work = 60 - 25 = 35 units.

•Days required by B alone = Remaining work / B's rate = 35 / 2 = 17.5 days.

Answer: 17.5 additional days

💡 Speed Shortcut: Check whether the question asks for "total days" (5 + 17.5 = 22.5) or "more days for remaining work" (17.5).

Common Exam Traps to Avoid

✕Adding days directly (e.g. 20 + 30 = 50 days) instead of combining daily rates.
✕Forgetting that a leak or outlet pipe possesses a negative efficiency.
✕Misinterpreting "A is twice as fast as B" — this means A takes half the time of B.

Interactive Practice Drill (3 Questions)

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Time, Work & Pipes/Cisterns Practice Drill

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1Time, Work & Pipes/Cisterns

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A can do a piece of work in 12 days, and B can do it in 24 days. Working together, in how many days can they complete the same work?

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