🗺️ Chapter Roadmap
1 The Core Concept
Time and Work have an Inverse (Opposite) Relationship. If you increase the number of workers, the time taken to finish the job decreases. If you have fewer workers, the job will take more time.
The "Man-Days" Logic: In exams, if 10 men take 5 days to build a wall, then 1 man will NOT take 0.5 days. He will take 50 days (10 × 5). This is because he has to do all the work by himself!
2 The "1 Day Work" Rule
The basic rule to solve any complex Time & Work problem is to find out how much work happens in exactly one day (or one hour/unit of time).
The Unitary Formula
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If a person takes 5 days to finish a whole job.
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Then in 1 day, that person finishes 15 part of the job.
- One Day Work = 1Total Days
3 ⚡ The "Work Together" Shortcut
Exam Question: "Person A takes x days to finish a job. Person B takes y days. How long will they take if they work together?" Use this formula to skip the fraction calculation:
Multiply the days on top • Add the days on bottom
📝 Solved Example:
Ali can paint a wall in 10 days ($x = 10$).
Asad can paint the same wall in 15 days ($y = 15$).
How long will it take if they work together?
4 Efficiency & Pipes (Deep Content)
🔥 The Efficiency Rule
Efficiency is Inversely proportional to Time. If A is twice as fast as B, he will take half the time B takes.
Ratio of Time taken: 1 : 2
🚰 Pipes & Cisterns
Exactly like Time & Work. Only difference: An inlet pipe is Positive (+) and a leakage pipe is Negative (-).
Together = xyx - y
🧠 Pro-Level Formula: M1D1 = M2D2
Used when comparing groups of workers.
Question: If 6 men can do a job in 12 days, how many days will 9 men take?
72 = 9x → x = 8 Days