SSC CGL Maths · Time and Work
Work Rates
A worker who finishes a job in n days does one n-th of it each day, so rates add when people work together and subtract when you need one worker's share.
Why this matters
Fifty-two questions in the bank, forty-six of them EASY: two or three people working together, one worker found from a team, the part of the job left after a few days, and pay shared by work done. Every later page in this chapter reuses the one-day rate, so make it automatic here.
Concept 1 of 4: Workers together: add the one-day rates
If Ravi paints a wall in 6 days, he paints a sixth of it each day. Two painters on the same wall each add their own share every day, so you add what each one does in a day. You never add the days.
Definition
- One day's work: a worker who needs days does of the job each day. Hours and minutes work the same way.
- Together: add the rates. Time together (sum of the rates).
- Two workers, fast route: time together , product over sum. It is safe for exactly two workers only.
- LCM units, fast route: take the job as the LCM of the given times. Each worker's daily units are that LCM divided by their own time, always whole numbers, and the time is units divided by the daily total. This is the quickest way for three workers.
- Output jobs (pages typed, items made) work the same way with real units: pages per hour add.
Working together
- ndays one worker needs alone
- a, b, cdays each worker needs alone
- Tdays needed when they work together
Worked example
P can finish a job in 12 days, Q in 20 days and R in 30 days. How many days do all three take working together?
Practice this conceptself-check · 4 quick reps
The same idea in a real exam question:
SSC CGL · 2023 · Tier I, 17 Jul 2023, Shift 1 · Q60Easy
Example 1 · Time and Work · Work Rates
A, B and C, working alone, can complete a job in 16, 24 and 36 days, respectively. In how many days can they complete the job if they work together?
Adding the days instead of the rates
Two workers taking 10 and 15 days do not take 25 days together, nor 12.5 days (the average). Together is always quicker than the faster worker alone: here days.
Using product over sum for three workers
is not the time for three workers. For 12, 20 and 30 days it gives about 116 days, while the true time is 6. For three or more workers, add the rates or use LCM units.
Concept 2 of 4: Part of the job done in a given time
Work done is rate times time, just as distance is speed times time. If the whole job takes 20 days, 5 days of it finish a quarter. Running the other way, if part of a job took some days, scale up to find the whole.
Definition
- Work done rate time for a worker who needs days and works days.
- Work left work done. For a team, use the team's daily rate, the sum of its members' rates.
- Part known, whole wanted: if a fraction of the job takes days, the whole job takes days, and any other fraction takes days.
- Fast route: when two workers are described by the parts they finish in the SAME number of days, add the parts directly. There is no need to find each whole time.
Work done and work left
- tdays worked
- ndays the worker needs for the whole job
- Wfraction of the job done
- ffraction of the job finished in d days
- ddays taken for that fraction
Worked example
P can finish a job in 10 days and Q in 14 days. They work together for 5 days. What fraction of the job is left?
Practice this conceptself-check · 4 quick reps
The same idea in a real exam question:
SSC CGL · 2025 · Tier I, 12 Sep 2025, Shift 1 · Q66Easy
Example 2 · Time and Work · Work Rates
A is able to complete a task in 15 days, while B takes 20 days to finish the same task. If they collaborate and work together for 4 days, what fraction of the work will still remain?
Marking the part done when the part left is asked
If a team does of a job in the days given, the part left is . SSC usually prints both fractions among the options, so read the last line of the question again before marking.
Scaling the days the wrong way
If of a job takes 18 days, the whole takes days, not . The whole job always takes longer than any part of it.
Concept 3 of 4: One worker's time from the team's time
A team's rate is the sum of its members' rates. Take away the members you know and what remains is the unknown worker's rate. When only pairs are given, each person sits in two of the pairs, so the three pair rates add to twice the whole team.
Definition
- One worker missing: rate of the missing worker team rate the known rates.
- Two people, fast route: if the pair takes days and the known worker days (), the other takes days.
- Pages or units: subtract pages per hour the same way, then time pages pages per hour.
- Three pairs given (A and B, B and C, C and A): add the three pair rates. The sum is twice the rate of all three, so halve it, then take away a pair to get one person.
- LCM units keep every step in whole numbers: take the job as the LCM of the pair times.
Finding one worker
- adays the pair takes together
- bdays the known worker takes alone
- xdays the other worker takes alone
- each worker's one-day rate
Worked example
A and B together can finish a job in 10 days. A alone takes 15 days. How long does B take alone?
Practice this conceptself-check · 4 quick reps
The same idea in a real exam question:
SSC CGL · 2025 · Tier I, 13 Sep 2025, Shift 2 · Q66Easy
Example 3 · Time and Work · Work Rates
A can lay railway track between two specified stations in 16 days, while B can complete the same task in 12 days. When C assists them, they manage to finish the job in just 4 days. How long would it take for C to complete the job on their own?
Forgetting to halve the pair total
When the times of A and B, B and C, and C and A are given, the sum of the three pair rates is twice the rate of all three, because each person appears in two pairs. Not halving doubles the team's speed and halves its time.
Subtracting the times
If a pair takes 10 days and one of them 15 days, the other does not take 5 days. Subtract rates: , so 30 days.
Concept 4 of 4: Sharing the pay by work done
The money is paid for the job, not for the days spent on it. Each person gets the same share of the money as the share of the work they did.
Definition
- Share of the pay share of the work done total pay.
- Everyone works the whole time: shares are in the ratio of the rates, . LCM units give this ratio at once as whole numbers.
- A helper joins: find what the named workers did in the days worked. The helper's share of the work is 1 minus theirs.
- Days matter only through the work they produce: a slow worker who works many days can earn more than a fast one who works a few.
Pay shared by work
Worked example
A can finish a job in 6 days, B in 9 days and C in 18 days. They do it together and are paid ₹4,200. What is B's share?
Practice this conceptself-check · 3 quick reps
The same idea in a real exam question:
SSC CGL · 2025 · Tier I, 14 Sep 2025, Shift 3 · Q62Moderate
Example 4 · Time and Work · Work Rates
A alone can complete a job in 12 days and B alone in 18 days. A and B agree to do the work for ₹ 7,200. With C's help they finish it in 5 days. How much should C be paid?
Sharing the pay in the ratio of days
Pay follows work, so it is shared in the ratio of the rates, which is the inverse of the days. When both work the whole time, a worker who needs 10 days earns more than one who needs 15.
Giving a helper an equal share
A helper who joins for all the days does not get an equal part of the money. His share is the work he did: 1 minus what the others did in those days.
Summary — formulas & gotchas at a glance
A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.
Formulas (4)
- Workers together: add the one-day rates
Working together
- Part of the job done in a given time
Work done and work left
- One worker's time from the team's time
Finding one worker
- Sharing the pay by work done
Pay shared by work
Watch out for (8)
- Adding the days instead of the rates→ Workers together: add the one-day rates
- Using product over sum for three workers→ Workers together: add the one-day rates
- Marking the part done when the part left is asked→ Part of the job done in a given time
- Scaling the days the wrong way→ Part of the job done in a given time
- Forgetting to halve the pair total→ One worker's time from the team's time
- Subtracting the times→ One worker's time from the team's time
- Sharing the pay in the ratio of days→ Sharing the pay by work done
- Giving a helper an equal share→ Sharing the pay by work done
Test yourself on Time and Work
20 past SSC CGL questions from this chapter, timed at 12 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.