Work is always considered as 1 unit (complete job). If A can complete work in 10 days, A's rate of work is 1/10 per day. This means A completes 1/10th of the total work each day
💡Key Rules
Work = Rate × Time. If multiple people work together, their rates add up. Total work is always 1 unit. Rate of work = 1/Time taken to complete the job
🔑Basic Formulas
- If A completes work in 'a' days, A's one day work = 1/a
- If A and B together complete work in 'd' days, (1/a + 1/b) = 1/d
- Time taken by A and B together = (a × b)/(a + b) days
- If A completes work in 'x' days and B in 'y' days, working together they complete in xy/(x+y) days
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Exam Patterns
What examiners ask — read before attempting PYQs
📋Common patterns include
two people working together, one person leaving midway, comparing efficiencies, and alternative work scenarios
⚡Shortcut Trick - LCM Method
Take LCM of all time periods given. This becomes total work. Then find individual rates by dividing LCM by individual time. This eliminates fractions and makes calculations faster
✏️Worked Example 1
1
A's one day work = 1/12
2
B's one day work = 1/18
3
Combined one day work = 1/12 + 1/18 = (3+2)/36 = 5/36
4
Time taken together = 36/5 = 7.2 days
Alternative (Shortcut): Time = (12 × 18)/(12 + 18) = 216/30 = 7.2 days
Worked Example 2: A and B together can complete work in 6 days. A alone can complete it in 10 days. In how many days can B alone complete the work?
1
Combined one day work = 1/6
2
A's one day work = 1/10
3
B's one day work = 1/6 - 1/10 = (5-3)/30 = 2/30 = 1/15
4
B alone can complete work in 15 days
Shortcut Formula: If A and B together complete work in T days and A alone in A days, then B alone takes: B = (A × T)/(A - T) days
Applying: B = (10 × 6)/(10 - 6) = 60/4 = 15 days
Most Common Trap: Students often add time instead of adding rates. Remember - when people work together, their RATES add up, not their TIME. If A takes 4 days and B takes 6 days, together they DON'T take 4+6=10 days. Instead, calculate 1/4 + 1/6 to find combined rate
⚠️Another Major Mistake
Forgetting that work is always 1 unit. Students sometimes assume work quantity changes, leading to wrong calculations. Always treat complete work as 1 unit regardless of the scenario
⚡Efficiency Trick
If A is twice as efficient as B, then A takes half the time B takes. If A:B efficiency ratio is 2:3, then their time ratio is 3:2 (inverse relationship)
→Negative Work Concept
Sometimes one person does work while another undoes it (like filling and emptying a tank). In such cases, subtract the rates instead of adding them.
If 8 workers can build a wall in 6 days, how many days will 12 workers take to build the same wall?
Practice 2easy
If 5 workers can build a wall in 18 days, how many days will 9 workers take to build the same wall (assuming all workers work at the same rate)?
Practice 3hard
A and B together can complete a project in 12 days. After working together for 4 days, A leaves and B completes the remaining work alone in 10 more days. In how many days can A alone complete the entire project?
Practice 4hard
Pipes A and B can fill a tank in 20 hours and 30 hours respectively. Pipe C can empty the full tank in 40 hours. If all three pipes are opened simultaneously, and after 5 hours pipe A is closed, how many more hours are needed to fill the tank?
Practice 5hard
X can do a job in 12 days, Y can do it in 18 days, and Z can do it in 36 days. They work together for some days, then Y and Z continue while X leaves. After X leaves, Y and Z work together for 6 more days to finish the job. For how many days did all three work together?
Practice 6hard
A contractor hired A, B, and C to complete a project. A works at 3 times the speed of C, and B works at 2 times the speed of C. If all three working together can finish the project in 8 days, how many days will it take for B alone to complete the project?
60-Second Revision — Basic Time & Work
Formula: Combined time = (a × b)/(a + b) for two people working together
Remember: Add RATES, never add TIME when people work together
Trap: Don't assume 4 days + 6 days = 10 days together
Quick method: Use LCM of times as total work to avoid fractions
Efficiency rule: Higher efficiency = Less time (inverse relation)
Standard approach: Find individual rates, add them, then find combined time
Check: Combined time should always be less than individual times