Time & Work

Time & Work questions become simple once you stop thinking in days and start thinking in "work done per day" — the efficiency method.

The efficiency method

If a person can finish a job in n days, their one-day work (efficiency) is 1/n of the job. Add efficiencies to combine workers; total time = 1 ÷ (combined efficiency).

Pipes and cisterns

Same idea — an inlet pipe adds to the work (fills the tank), an outlet pipe subtracts from it (empties the tank).

Worked Example 1

An UdaanPath content writer, A, can draft one full mock-test paper (100 questions) in 10 days. Another writer, B, takes 15 days for the same paper. If they split the work and draft it together, how long will it take?

A's efficiency = 1/10, B's efficiency = 1/15. Combined = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6. Together they take 6 days.

Worked Example 2

Writer A can draft a paper alone in 12 days. Working together, A and B finish it in 8 days. How long would B alone take?

B's efficiency = 1/8 − 1/12 = 3/24 − 2/24 = 1/24. B alone takes 24 days.

Worked Example 3 — pipes

Pipe A fills a tank in 6 hours, pipe B empties it in 9 hours. If both are opened together, how long to fill the tank?

Net efficiency = 1/6 − 1/9 = 3/18 − 2/18 = 1/18. Tank fills in 18 hours.

Common mistakes

Don't average the number of days directly (e.g. assuming two workers taking 10 and 15 days together take 12.5 days) — always work through efficiencies (1/n), never raw day-counts.

Practice Set

1. A can finish a job in 20 days, B in 30 days. In how many days will they finish it together?
2. A, B and C can complete a work in 10, 15 and 30 days respectively. Find the time taken if all three work together.
3. A pipe fills a tank in 5 hours. Due to a leak, it takes 6 hours. How long would the leak alone take to empty the full tank?
4. An UdaanPath writer can draft a full question bank in 18 days. She works for 6 days, then a colleague finishes the rest in 12 days. In how many days could the colleague alone have finished the whole bank?