Study Guides/Physics/Time and Work Problems
Study Guide · Physics

Time and Work: Formula and Solved Examples

Time and Work is a fundamental topic in Quantitative Aptitude for competitive exams like SSC, Banking, and Railway. The core concept is simple: if a person does more work per day, they finish faster.

Question (Click to Flip)

What is the formula for time and work problems?

Answer

If a person completes work in 'n' days, they do 1/n of the work per day. For two people working together, add their per-day fractions: Combined work per day = 1/A + 1/B. The total time = 1 ÷ (combined per day work).

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Key Facts

Formula: If work done in n days → 1-day work = 1/n.

To find combined time: Add 1-day fractions, then take reciprocal.

Shortcut: Use LCM method for fast calculation in exams.

The Core Formula

Work = Rate × Time

The key idea: If a person completes a job in 'n' days, then in 1 day they complete 1/n of the total work.

  • Person A finishes in 10 days → Does 1/10 of work per day.
  • Person B finishes in 15 days → Does 1/15 of work per day.
  • Together, in 1 day they do: 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 of work.
  • So together they finish in 6 days.

Solved Example

Q: A can finish a job in 12 days and B in 18 days. How long if they work together?

A's 1-day work = 1/12 B's 1-day work = 1/18

Combined 1-day work = 1/12 + 1/18 = 3/36 + 2/36 = 5/36

Time to finish together = 36/5 = 7.2 days (7 days 5 hours)

LCM Method (Shortcut)

Use LCM of the number of days as 'Total Work':

  • A: 12 days, B: 18 days → LCM = 36 units.
  • A's efficiency = 36/12 = 3 units/day.
  • B's efficiency = 36/18 = 2 units/day.
  • Combined = 3 + 2 = 5 units/day.
  • Time = 36/5 = 7.2 days.

Questions and Answers

What is the formula for time and work problems?+

If a person completes work in 'n' days, they do 1/n of the work per day. For two people working together, add their per-day fractions: Combined work per day = 1/A + 1/B. The total time = 1 ÷ (combined per day work).

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