In this guide
Most students first learn time and work with fractions: A does 1/12 of the job in a day, B does 1/18, together 1/12 + 1/18 = 5/36… This works, but fractions slow you down and invite errors. The LCM method is faster: assume the job has a convenient number of units, and work only with whole numbers.
The LCM method
Worked example: A can complete a job in 12 days and B in 18 days. How long will they take together?
- Total work = LCM(12, 18) = 36 units.
- A's rate = 36/12 = 3 units a day; B's rate = 36/18 = 2 units a day.
- Together = 5 units a day.
- Time = 36/5 = 7.2 days.
Finding one person's time
Worked example: A and B together finish a job in 10 days. A alone takes 15 days. How long does B take alone?
Total = LCM(10, 15) = 30 units. A + B = 3 units/day; A = 2 units/day, so B = 1 unit/day. B alone takes 30 days.
Efficiency
If A is twice as efficient as B, A takes half the time B takes.
Worked example: A is 50% more efficient than B. B takes 24 days. How long does A take?
Efficiency ratio A : B = 3 : 2, so the time ratio = 2 : 3. A takes 24 × 2/3 = 16 days.
Joining and leaving
Worked example: A can do a job in 20 days and B in 30 days. They work together for 6 days, then A leaves. How long does B take to finish?
Total = 60 units. A = 3/day, B = 2/day. In 6 days: 5 × 6 = 30 units. Remaining 30 units by B alone: 15 days.
Alternate days
Worked example: A takes 10 days and B takes 15 days. They work on alternate days, starting with A. In how many days is the job done?
Total = 30 units. A = 3/day, B = 2/day. Every 2-day cycle does 5 units. After 5 cycles (10 days): 25 units. Day 11: A does 3 → 28. Day 12: B does 2 → 30. Job done in 12 days.
Men, days and hours
M₁ × D₁ × H₁ / W₁ = M₂ × D₂ × H₂ / W₂
where M = workers, D = days, H = hours per day, W = work.
Worked example: 12 workers working 8 hours a day complete a wall in 10 days. How many days will 16 workers take, working 6 hours a day, to build the same wall?
12 × 10 × 8 = 16 × D × 6 → 960 = 96D → D = 10 days.
Wages
Wages are shared in proportion to work done (or efficiency when they work the same time).
Worked example: A and B can do a job in 6 and 8 days. Together they earn ₹2,800. Find A's share.
Efficiency A : B = 1/6 : 1/8 = 4 : 3. A's share = 4/7 × 2,800 = ₹1,600.
Pipes and cisterns
Pipes work like workers — inlets add work, outlets or leaks subtract it.
Worked example: Pipe A fills a tank in 12 hours and pipe B in 15 hours. Pipe C empties it in 20 hours. If all three are opened, how long will the tank take to fill?
Total = LCM(12, 15, 20) = 60 units. A = +5, B = +4, C = −3. Net = 6 units/hour. Time = 10 hours.
Worked example (leak): A pipe fills a tank in 6 hours, but because of a leak it takes 8 hours. How long would the leak take to empty a full tank?
Total = 24 units. Pipe = 4/hour; with leak = 3/hour; leak = 1/hour. The leak empties the tank in 24 hours.
Common traps
| Trap | Correct approach |
|---|---|
| Adding times instead of rates | Add daily work, not days |
| Forgetting a leak is negative | Subtract outlet or leak rates |
| Wrong efficiency–time link | Efficiency and time are inversely proportional |
Practice
- A can do a job in 15 days and B in 20 days. How long will they take together?
- A and B together can do a job in 12 days; B alone in 20 days. How long does A take alone?
- 20 men can build a road in 15 days working 8 hours a day. How many men are needed to build it in 10 days working 10 hours a day?
- A is thrice as efficient as B and together they finish a job in 15 days. How long would A take alone?
- Pipes A and B fill a tank in 10 and 15 hours. Pipe C empties it in 30 hours. How long will all three take together?
- A and B can do a job in 10 and 15 days. They earn ₹4,500 together. Find B's share.
Answers: 1. 60/7 ≈ 8.57 days. 2. 30 days. 3. 24 men. 4. 20 days. 5. 7.5 hours. 6. ₹1,800.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Staff Selection Commission website .
Get the next SSC CGL guide by email
New guides every week. No spam, unsubscribe any time.