Time and work questions appear in almost every SSC, banking, railway and campus placement test. Enter how long each person takes alone to see how long they take together, solved with both the one-day-work method and the LCM shortcut.
Enter the days each person needs alone.
Leave C as 0 if there are only two people.
Read the days needed together.
Together: 1/T = 1/a + 1/b (+ 1/c)
Two people: T = ab ÷ (a + b)
Time and work is one of the most tested chapters in quantitative aptitude. SSC, IBPS and SBI bank exams, railway recruitment tests and campus placement papers all include questions like 'A can finish a job in 12 days and B in 18 days; how long will they take together?' This calculator solves such questions for two or three workers.
It shows two methods side by side. The one-day-work method adds each person's fraction of the job per day. The LCM method, taught in most coaching classes, assumes the total work is the LCM of the days so that every daily rate is a whole number of units.
Enter the days each person needs alone, and leave C as 0 if there are only two workers.
1. For each worker who finishes alone in d days, write the daily rate as 1/d of the job.
2. Add the rates of everyone working together: R = 1/a + 1/b (+ 1/c).
3. Time together T = 1 ÷ R.
4. For two workers, use the shortcut T = ab ÷ (a + b).
5. LCM method: let total work = LCM of the days. Each worker's units per day = LCM ÷ their days.
6. Add the units per day and divide the total work by that sum to get T.
7. For someone who leaves or joins midway, compute the work done in each phase separately and add the phases.
The core idea is that work rates are additive, while times are not. If A does 1/12 of the job per day and B does 1/18, together they do 1/12 + 1/18 = 5/36 per day. The time is the reciprocal, 36/5 = 7.2 days. Adding the times (30 days) or averaging them (15 days) makes no sense, because two people working together must finish faster than either alone. The combined time is always less than the fastest worker's time.
Choosing the total work as a common multiple of all the days makes every daily output a whole number. With 12 and 18 days, LCM = 36 units, so A does 3 units a day and B does 2. Together they do 5 units a day and take 36 ÷ 5 = 7.2 days. Any common multiple would work; the LCM keeps numbers smallest. The method is identical to the fraction method, just scaled, so it avoids fraction arithmetic under exam time pressure.
The model assumes each person works at a constant rate, their efforts do not interfere, and the job can be split freely. Real teams can be slower because of coordination, or faster if they share tools. Exam questions sometimes add efficiency statements, such as 'A is twice as efficient as B', which means A's rate is double and A needs half the days. Wages in such questions are split in the ratio of work done, which equals the ratio of rates when everyone works the same number of days.
A painting contractor in Jaipur knows that Ramesh alone can paint a house in 10 days, Suresh in 15 days and their apprentice Mohan in 30 days. He wants to know how long all three take together.
One day's work of each person: A = 1/10, B = 1/15, C = 1/30
Work done together in one day: 1/10 + 1/15 + 1/30 = 0.2
Days to finish together: 1 ÷ 0.2 = 5 days
LCM method (total work = LCM of days): Total work = LCM(10, 15, 30) = 30 units Per day: A 3, B 2, C 1 → together 6 units/day 30 ÷ 6 = 5 days
Answer: Days to finish together 5 days; Work done per day 20%
Adding or averaging the days instead of adding the daily rates.
Forgetting to take the reciprocal at the end, and reporting the combined rate as the time.
Misreading 'twice as efficient' as 'takes twice as long'.
In leave-midway questions, applying the combined rate to the whole job instead of splitting it into phases.
Splitting wages by days worked alone rather than by work actually done.
Practising SSC, banking and railway aptitude questions.
Campus placement test preparation.
Estimating completion time when several workers or machines share a task.
Dividing payment among workers in proportion to their contribution.
What is the shortcut for two people?
T = ab ÷ (a + b). For 12 and 18 days, T = 216 ÷ 30 = 7.2 days.
How do I handle someone who leaves midway?
Work out the part finished while everyone worked, then divide the remaining work by the rate of those who stay.