Why this topic matters · 8 min read
Time and Work is a guaranteed 2-3 question topic in SSC CHSL every year. Questions test how fast workers complete jobs alone or together, pipes filling tanks, and work efficiency comparisons. The difficulty is light to moderate — mostly one-step or two-step calculations. Master the LCM method and you can solve most questions in under 60 seconds.
Core Concept: Work as a Unit
Think of the total work as one complete job — like filling one tank or building one wall. If a person finishes the job in N days, then in ONE day they do 1/N of the total work. This fraction is called their 'one-day work' or efficiency. The whole game is about adding or comparing these fractions.
- If A finishes work in N days, A's 1-day work = 1/N
- If A and B work together, combined 1-day work = 1/A + 1/B
- Time taken together = 1 divided by (combined 1-day work)
- More workers = less time (inverse relationship)
- Work = Efficiency x Time — always
Key formulas
Together formula (2 people)
Time together = (A x B) / (A + B)
When: When two people work together and you know their individual times
One-day work
Work done in 1 day = 1 / Total days
When: Starting point for every Time and Work problem
Remaining work
Remaining work = 1 - (work already done)
When: When one person starts, works for some days, then another joins
Worked examples
A finishes a job in 12 days, B in 15 days. Together: (12 x 15)/(12 + 15) = 180/27 = 6.67 days, roughly 6 days 16 hours.
A and B together finish in 10 days. A alone takes 15 days. B alone = ? Use: 1/B = 1/10 - 1/15 = 3/30 - 2/30 = 1/30. So B alone takes 30 days.
LCM Method (Fastest Trick for SSC)
Instead of working with messy fractions, assume the total work = LCM of all given days. Then convert each person's time into their daily work units (called efficiency). Add efficiencies, divide total work by combined efficiency. This avoids fractions entirely and is the go-to method in exams.
- Total work = LCM of all individual times
- Efficiency of a person = Total Work / Their individual days
- Combined efficiency = sum of individual efficiencies
- Time together = Total Work / Combined Efficiency
- Works perfectly for 3 or more people too
Key formulas
LCM Method
Total Work = LCM(days1, days2, ...); Efficiency = Total Work / Individual Days; Time = Total Work / Sum of Efficiencies
When: Always — especially when 3 or more workers are involved
Worked example
A takes 12 days, B takes 18 days. LCM(12,18) = 36. A's efficiency = 36/12 = 3 units/day. B's efficiency = 36/18 = 2 units/day. Together = 5 units/day. Time = 36/5 = 7.2 days.
Work Done in Parts (Mid-way Problems)
A very common SSC pattern: A works alone for a few days, then B joins (or leaves). You calculate how much work is done in the solo phase, subtract from total, and find the remaining time with combined effort. Always track remaining work carefully.
- Find work done in the solo phase: days x efficiency
- Remaining work = Total - work already done
- Time for remaining work = Remaining Work / New combined efficiency
- Total time = solo days + remaining days
- Read the question carefully — sometimes B leaves, sometimes B joins
Worked example
A takes 20 days, B takes 30 days. A works alone for 5 days, then B joins. LCM = 60. A's efficiency = 3, B's = 2. Work done by A in 5 days = 5 x 3 = 15 units. Remaining = 60 - 15 = 45 units. Together = 5 units/day. Remaining time = 45/5 = 9 days. Total = 5 + 9 = 14 days.
Pipes and Cisterns
This is just Time and Work with water. A pipe that fills a tank is like a worker doing positive work. A pipe that drains (outlet) is like a worker doing negative work — subtract its efficiency. The tank getting full is the total job = 1 (or LCM units).
- Inlet pipe fills = positive efficiency
- Outlet pipe drains = negative efficiency
- Net efficiency = sum of inlets minus sum of outlets
- If net efficiency is negative, tank will never fill
- Use the same LCM method as regular work problems
Key formulas
Net filling rate
Net rate = (1/inlet time) - (1/outlet time)
When: When both a filling pipe and a draining pipe are open simultaneously
Worked example
Pipe A fills in 10 hrs, Pipe B drains in 15 hrs. Both open: Net = 1/10 - 1/15 = 3/30 - 2/30 = 1/30. Tank fills in 30 hours.
Efficiency and Ratio Problems
Sometimes SSC gives you ratios of efficiency (A is twice as fast as B) instead of actual days. If A is twice as efficient, A takes half the time. Efficiency and time are inversely proportional. You can assign numbers: if ratio is 2:3, assign days as 3:2 (flip the ratio).
- Efficiency ratio 2:3 means time ratio 3:2 (always flip)
- If A is twice as fast as B, A takes half B's time
- Assign convenient numbers based on flipped ratio
- Then solve normally using LCM method
- Wages are split in the ratio of work done (efficiency ratio)
Key formulas
Efficiency-Time relation
Efficiency is inversely proportional to Time: E1/E2 = T2/T1
When: When efficiency ratio is given and you need to find individual times
Wage distribution
Wage share = (Individual efficiency / Total efficiency) x Total wage
When: When workers are paid based on work done
⚠ Common mistakes to avoid
- Using the together formula (A x B)/(A + B) for three people — this only works for two people. Use LCM method for three or more.
- Forgetting that outlet pipes are NEGATIVE — students add all pipe rates instead of subtracting the drain pipe.
- In mid-way problems, students forget to ADD the solo days to the remaining days and give only the remaining time as final answer.
- Flipping efficiency and time ratio wrong — if A:B efficiency is 3:2, time is 2:3, not 3:2. Many students forget to flip.
- Confusing 'work remaining' with 'work done' — always write out: Remaining = Total minus Done, never guess.
🧠 Memory aids
- LCM is your best friend: Let's Calculate Magically — assume total work = LCM of all days, then just work with whole numbers.
- PIPE rule: Inlet = Plus, Outlet = miOnus (P for Plus, O for minus — PO rule).
- Efficiency-Time flip: Think of a car — faster speed means less time. Ratio of speeds flips to ratio of time. Same here.
- Together formula shortcut: Two people A and B together = Product over Sum (POS). (A x B) / (A + B). Remember POS like 'point of sale'.
🎯 SSC CHSL exam tips
- SSC CHSL typically has 2 to 3 questions from this topic. Expect one standard 'together' question, one mid-way (A starts, B joins) question, and possibly one pipes and cisterns question.
- LCM method saves 30-40 seconds per question compared to fraction method. Practice it until it is automatic — it is the single most important trick here.
- Pipes and cisterns in CHSL are rarely difficult — usually one inlet and one outlet, straightforward net rate calculation.
- Wage-sharing questions appear occasionally — remember wages split in ratio of efficiency (work done), not ratio of days taken.
- These questions are solvable in 45-90 seconds with practice. Never leave them — they are among the most scoring questions in the Quant section.
Q1 · medium · PYQ 2021
Annu can complete a piece of work in 22 days. Shama is 60% more efficient than Annu. How many days does Shama along take to complete the same piece of work?
- 36(2/3)
- 13(3/4)
- 13(1/5)
- 35(1/3)
Q2 · medium · PYQ 2025
10 men can complete a piece of work in 8 days. How many men are required to complete the same work in 5 days?
- 20 men
- 16 men
- 12 men
- 14 men
Q3 · medium · PYQ 2025
If 8 men can do a piece of work in 14 days, the time taken by 12 men to do the same piece of work will be:
- 7.5 days
- 8 days
- 8.5 days
- 9.33 days
Q4 · medium · PYQ 2023
A can finish a work in 15 days, B can finish the same work in 25 days. They work together for 5 days. The rest of the work is finished by A and C in 4 days. Then C alone can finish the work in:
- 21 days
- 20 days
- 24 days
- 18 days
Q5 · medium · PYQ 2024
Riya and Sangeeta can finish a work in 6 days and 8 days, respectively. Riya started the work alone and then after 3 days, Sangeeta joined Riya. They both finish the remaining work. How long did the total work last?
- 4(2/7) days
- 4(3/7) days
- 4(4/7) days
- 4(5/7) days