Time and Work Questions for Bank Exams: The Short Answer
Bank prelims arithmetic usually carries one or two time and work questions, often written as a pipe-and-tank or "leak" problem. The fastest way to solve almost all of them is the LCM (total work) method: take the total work as the LCM of the given days or hours, turn every person or pipe into "units per day", then add or subtract the rates. No fractions, and every question below takes three lines.
Key takeaway: Total work = LCM of the times. Rate = total ÷ time. Together, add the rates; for a leak or outlet pipe, subtract its rate. Every answer on this page was computed and checked in Python.
Time and Work Formulas (Quick Table)
| Situation | Formula |
|---|---|
| A alone takes a days | A's one-day work = 1/a |
| A and B together | Time = ab ÷ (a + b) |
| A, B and C together | Time = 1 ÷ (1/a + 1/b + 1/c) |
| Efficiency | Time is inversely proportional to efficiency |
| Men, days, hours | M1 × D1 × H1 = M2 × D2 × H2 (same work) |
| Pipe fills in f hours, with a leak in w hours | Leak empties the full tank in fw ÷ (w − f) hours |
| Two inlets and one outlet | Time = 1 ÷ (1/p + 1/q − 1/r) |
| Wages for a shared job | Share in the ratio of one-day work |
The LCM Method Step by Step
- Write the total work as the LCM of all the given times (days or hours).
- Find each rate: total ÷ time. A pipe that empties gets a minus sign.
- Combine the rates for whoever is working in that period.
- Divide the work left by the combined rate.
Example: A takes 12 days and B takes 18 days. LCM = 36 units, so A does 3 and B does 2 units a day, together 5 units a day, and 36 ÷ 5 = 7 1/5 days.
Time and Work Solved Questions (Bank Exam Pattern)
Q1. Ravi can finish a job in 12 days and Neha in 18 days. In how many days will they finish it working together?
Total work = LCM(12, 18) = 36 units. Ravi does 36/12 = 3 units a day, Neha 36/18 = 2. Together 5 units a day, so time = 36/5 = 7 1/5 days. (Shortcut: ab/(a + b) = 216/30.)
Q2. A, B and C can do a work in 10, 15 and 30 days respectively. All three start together, but A leaves after 2 days. In how many days in all is the work finished?
Total = LCM = 30 units; daily work A = 3, B = 2, C = 1. In 2 days all three do 6 × 2 = 12 units. Remaining 18 units are done by B and C at 3 units a day in 6 days. Total time = 2 + 6 = 8 days.
Q3. A is 50% more efficient than B. B alone can finish a work in 30 days. In how many days can A and B together finish it?
Efficiency ratio A : B = 150 : 100 = 3 : 2, so time ratio = 2 : 3. A alone takes 30 × 2/3 = 20 days. Together: (20 × 30)/(20 + 30) = 12 days.
Q4. 24 men working 8 hours a day finish a work in 15 days. In how many days will 20 men working 9 hours a day finish the same work?
M1 × D1 × H1 = M2 × D2 × H2 ⇒ 24 × 15 × 8 = 20 × D2 × 9 ⇒ D2 = 2880/180 = 16 days.
Q5. A pipe can fill a tank in 10 hours. Because of a leak at the bottom, it takes 12 hours to fill the tank. In how many hours can the leak alone empty the full tank?
Take the tank as LCM(10, 12) = 60 units. Pipe fills 6 units/hour; with the leak the net rate is 5 units/hour, so the leak removes 1 unit/hour. Leak empties 60 units in 60 hours. (Shortcut: fw/(w − f) = 120/2.)
Q6. Pipes A and B can fill a tank in 12 hours and 15 hours. Pipe C can empty the full tank in 20 hours. If all three are opened together, in how many hours will the empty tank be full?
Tank = LCM(12, 15, 20) = 60 units. A fills 5, B fills 4, C empties 3 units per hour. Net = 5 + 4 − 3 = 6 units/hour. Time = 60/6 = 10 hours.
Q7. A can finish a work in 20 days and B in 30 days. They work together and get ₹6,000 for the whole work. What is A's share?
Wages are shared in the ratio of work done per day: 1/20 : 1/30 = 30 : 20 = 3 : 2. A's share = 6,000 × 3/5 = ₹3,600.
Q8. A can do a work in 6 days and B in 12 days. They work on alternate days, A starting on the first day. In how many days is the work finished?
Total = 12 units; A does 2 units and B does 1 unit a day, so every 2-day pair gives 3 units. 12/3 = 4 pairs exactly, so the work ends on day 8 (the last day is B's).
Common Mistakes in Time and Work Questions
- Adding days instead of rates. 12 days and 18 days together is not 30 days; add the one-day work.
- Forgetting the minus sign for a leak. A leak or outlet pipe works against the inlet.
- Using efficiency directly as time. 50% more efficient means time is 2/3, not 1/2.
- Missing the "same work" condition in M × D × H. If the second job is twice as big, double the right-hand side.
Time and Work Practice Questions
- A can do a work in 15 days and B in 10 days. Working together, how long will they take?
- A pipe fills a tank in 6 hours; with a leak it takes 8 hours. How long will the leak take to empty the full tank?
- 18 workers finish a job in 20 days. How many days will 24 workers take (same hours a day)?
- Pipes A and B fill a tank in 10 and 12 hours; pipe C empties it in 15 hours. With all three open, how long to fill the empty tank?
- A is 25% more efficient than B, who takes 25 days alone. How long does A take alone?
Answers:
- 6 days
- 24 hours
- 15 days
- 8 4/7 hours
- 20 days
Time and Work FAQs
Which method is fastest for bank prelims?
The LCM (total work) method. It turns every question into whole-number rates, so you can add and subtract without fractions.
Are pipes and cisterns part of time and work?
Yes. A pipe is a worker that fills (positive rate) and a leak or outlet is a worker that empties (negative rate). The same LCM method works.
How many time and work questions come in IBPS and SBI prelims?
There is no fixed number. Arithmetic word problems (time and work, speed, profit, ages, interest and others) share the arithmetic part of the Quantitative Aptitude or Numerical Ability section, so practise them as a group.
Practice Next
- Tests: IBPS PO Arithmetic Word Problems Test 03, IBPS Clerk Arithmetic Word Problems Test 03, IBPS RRB Clerk Arithmetic Mock Test 04, SBI Clerk Arithmetic Mock Test 01, SBI Clerk Time and Work Mock Test 01.
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