In this guide
Most students first learn time and work with fractions: A does 1/10 of the job a day, B does 1/15, add them and invert. It works, but the fractions slow you down and invite slips. The total work method avoids them. Assume the job is made of a convenient number of units (the LCM of the given days), and everything becomes whole numbers.
This one method covers every standard setup SSC CHSL uses: people working together, someone leaving midway, alternate days, pipes filling and emptying a tank, and wages shared by work done.
The total work method, and why it works
- Take the total work = LCM of the given times.
- Find each worker's units per day = total work ÷ their time.
- Add rates for people working together, subtract for anyone (or anything) undoing work.
- Time = work to be done ÷ combined rate.
Why: the size of the job doesn't change the answer, only the units. Choosing the LCM makes every rate a whole number, so you never add fractions. It is the same idea as taking 100 as the base in percentage questions.
Efficiency and time are inverse
If A is twice as efficient as B, A takes half as long. More generally, for the same job, efficiency ratio = inverse of time ratio. If A and B take 10 and 15 days, their efficiencies are in the ratio 15 : 10, which is 3 : 2.
"A is 50% more efficient than B" means efficiency 3 : 2, so time 2 : 3.
Men, days and hours
For the same job, M₁ × D₁ × H₁ = M₂ × D₂ × H₂. If the jobs differ, divide each side by its work: M₁D₁H₁/W₁ = M₂D₂H₂/W₂.
Why: the total effort (one worker's hour as the unit) needed for a job is fixed. More workers or longer hours mean fewer days, in exact proportion.
Pipes and cisterns
Treat filling a tank as a job. Inlet pipes add work; outlets and leaks subtract it. A leak is just a worker with a negative rate.
Wages
Wages are shared in the ratio of work done, not time spent. If everyone works the same number of days, that is simply the ratio of their efficiencies.
Seven worked questions
Q1. A can build a wall in 10 days and B in 15 days. How long will they take together?
Total = LCM(10, 15) = 30 units. A = 3/day, B = 2/day, together 5/day. Time = 30 ÷ 5 = 6 days.
Q2. A and B together finish a job in 8 days. A alone takes 12 days. How long would B take alone?
Total = 24 units. A + B = 3/day and A = 2/day, so B = 1/day. B alone takes 24 days.
Q3. A can finish a job in 12 days and B in 18 days. They work together for 4 days, then A leaves. How long does B take to finish?
Total = 36 units. A = 3/day, B = 2/day. In 4 days they do 20 units. The remaining 16 units at 2/day take 8 days.
Q4. A can do a job in 6 days and B in 9 days. They work on alternate days, A starting. In how many days is the job done?
Total = 18 units. A = 3, B = 2, so each two-day cycle does 5 units. Three cycles (6 days) do 15 units, leaving 3. On day 7 A does exactly 3. Answer: 7 days.
Q5. 15 workers can dig a trench in 12 days working 8 hours a day. How many days will 20 workers take working 6 hours a day?
15 × 12 × 8 = 20 × D × 6, so 1,440 = 120D and D = 12 days.
Q6. Pipes A and B fill a tank in 6 and 8 hours. An outlet empties it in 12 hours. If all three are open, how long does the tank take to fill?
Total = 24 units. A = +4, B = +3, outlet = −2, net +5 an hour. Time = 24 ÷ 5 = 4.8 hours, which is 4 hours 48 minutes.
Q7. A and B can do a job in 12 and 15 days. With C's help, the three finish it in 5 days and are paid ₹1,800. Find C's share.
Total = 60 units. A = 5/day, B = 4/day, and all three together = 60 ÷ 5 = 12/day, so C = 3/day. In 5 days C does 15 of the 60 units. C's share = 15/60 × 1,800 = ₹450.
Quick checks
| Situation | Check |
|---|---|
| Two people together | Answer is less than the faster one's time |
| A leak slows a pipe | Leak alone takes longer than the pipe alone |
| Alternate days | Check whether the last day is a full day or a part-day |
| Wages | Shares add up to the total paid |
| Man-days | More workers means fewer days, never more |
Common mistakes
| Mistake | Fix |
|---|---|
| Adding times instead of rates | Add units per day, then divide |
| Forgetting that a leak subtracts | Give outlets and leaks a negative rate |
| Sharing wages by days worked | Share by work done |
| Treating "50% more efficient" as 50% less time | Efficiency 3 : 2 means time 2 : 3 |
| Ignoring hours per day in man-day questions | Include H on both sides |
Practice
- A can do a job in 20 days and B in 30 days. How long will they take together?
- A and B together take 6 days; B alone takes 10 days. How long does A take alone?
- 12 men can finish a job in 15 days. How many men are needed to finish it in 9 days?
- Pipe A fills a tank in 10 hours and pipe B empties it in 15 hours. If both are open, how long does the tank take to fill?
- A and B can do a job in 8 and 12 days and are paid ₹5,000 for it. Find B's share.
- A can do a job in 20 days and B in 25 days. They work together for 5 days, then B leaves. How long does A take to finish?
- Pipes A and B fill a tank in 12 and 15 hours, and pipe C empties it in 20 hours. If all three are open, how long does the tank take to fill?
- A is 50% more efficient than B. Together they finish a job in 18 days. How long would A take alone?
Answers:
- 12 days. Total 60: A = 3, B = 2, so 60 ÷ 5.
- 15 days. Total 30: A + B = 5, B = 3, so A = 2 and takes 30 ÷ 2.
- 20 men. 12 × 15 = M × 9.
- 30 hours. Total 30: +3 − 2 = +1 an hour.
- ₹2,000. Efficiency A : B = 3 : 2, so B gets 2/5 of 5,000.
- 11 days. Total 100: A = 5, B = 4. In 5 days they do 45, leaving 55 for A at 5 a day.
- 10 hours. Total 60: +5 + 4 − 3 = 6 an hour.
- 30 days. Efficiency 3 : 2, so the job is 5 × 18 = 90 units and A takes 90 ÷ 3.
What to do next
- Solve every example here with the LCM method, even the ones you could do in your head.
- Do 10 pipes-and-leaks questions, marking outlets with a minus sign before you start.
- Practise five alternate-day questions and check whether the last day is full or partial.
- Move on to speed and distance, which uses the same rate × time logic, and revise ratio for the efficiency questions.
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 .
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