समय और कार्य की मूल बातें
Time and Work Basics
Time and work is among the most predictable scoring blocks in SBI Clerk, and the whole topic rests on one idea: if a person finishes a job in n days, they complete 1/n of it in a single day. Convert every worker into a per-day fraction, add the fractions when they work together, and the answers fall out. The LCM method makes even that fraction work unnecessary, turning the topic into quick whole-number arithmetic that you can finish well inside a minute.
Work Done Per Day
Treat the whole job as 1 unit. A worker who takes 10 days does 1/10 of the job each day; one who takes 15 days does 1/15 each day. This per-day rate is the only quantity you ever need, because the time to finish is simply 1 divided by the combined rate. Whenever a question gives days, silently flip it into a per-day fraction, and whenever it gives a rate, flip it back into days — this two-way habit answers most basic work sums directly, with no equation to set up.
One day's work = 1 / (days to finish) Days = 1 / (one day's work)
The LCM Method
Fractions slow you down, so replace the whole job with a convenient number of units: the LCM of the given days. If A takes 10 days and B takes 15, let total work = LCM(10, 15) = 30 units. Then A does 30/10 = 3 units a day and B does 30/15 = 2 units a day. Now everything is whole numbers, with no fractions at all. This LCM trick is the single biggest speed gain in the entire topic and should be your default for every combined-work question you meet.
Combined Work
When people work together, add their per-day outputs. Continuing the LCM example, A and B together do 3 + 2 = 5 units a day, so they finish the 30-unit job in 30/5 = 6 days. If a worker leaves partway, count the units done so far and divide the remaining units by whoever is still working. Because you are adding and dividing whole numbers rather than juggling fractions, combined-work questions become almost mechanical once the total is set as the LCM of the days.
✗ Adding the days: 10 + 15 = 25 days together | ✓ Adding the rates: 3 + 2 = 5 units/day, so 30/5 = 6 days
Solved Examples
Example 1: A does a job in 12 days, B in 6 days. Total = LCM = 12 units; A = 1/day, B = 2/day, together 3/day, so 12/3 = 4 days. Example 2: A and B together finish in 8 days, A alone in 12. Take total = LCM(8, 12) = 24; together they do 3/day and A does 2/day, so B does 3 − 2 = 1/day, and B alone takes 24 days. The LCM keeps every step in whole numbers.
| Given | Convert to | Then |
|---|---|---|
| Days to finish | LCM units per day | Add rates for a team |
| Team rate | 1 / rate | Days to finish together |
| Worker leaves early | Units already done | Remaining ÷ remaining workers |
The Man-Days Concept
A closely linked idea is man-days: the total work equals the number of workers multiplied by the days they take, and this product stays constant for the same job. If 8 workers finish in 15 days, the job is 120 man-days, so 10 workers finish the same job in 120/10 = 12 days. This lets you scale the workforce up or down in a single line. Watch for questions that change the number of workers midway; split the job into segments, compute man-days for each, and the totals still add up cleanly.
यदि कोई काम n दिन में पूरा होता है तो एक दिन में 1/n काम होता है। कुल काम को दिनों के LCM के बराबर इकाई मान लें ताकि भिन्न न रहें। साथ काम करने पर दरें जोड़ें। कुल कार्य = श्रमिक × दिन (man-days) स्थिर रहता है।
Exam Pointer — SBI Clerk sets 2–3 time-and-work questions per paper, usually easy if you use the LCM method. Expect a combined-work sum, a worker-leaves-midway sum, or a man-days scaling question. The examiner's favourite trap is candidates adding days instead of rates, so always convert to per-day units first and add those, never the days.
60-Second Recap
- One day's work = 1 / days to finish.
- Set total work = LCM of the days to kill fractions.
- Working together, add the per-day rates.
- Man-days = workers × days stays constant for a job.