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