Time and work for IBPS Clerk

Time and work questions ask how long a job takes when people, machines or pipes work together, alone, in turns, or with someone leaving partway. The clerk exam tends to keep these at a friendly level: whole-number days, two or three workers, one twist. That makes them good marks if your method is fast and clean.

There are two ways to solve every question. The fraction method is the textbook one. The total-work (LCM) method avoids fractions altogether and is quicker in the exam hall.

The two methods

One-day work. If A finishes a job in 10 days, A does 1/10 of it each day. For people working together, add their fractions. The time taken is 1 ÷ (combined fraction).

Total work (LCM). Take the total work as the LCM of the individual times, measured in "units". Each person's daily output is then total ÷ their days, a whole number. Add outputs for people working together, and divide the total by the combined output.

Why the LCM method works: the size of the job is arbitrary. Choosing it as the LCM of the days just makes every daily rate a whole number. The ratio of rates, and so every answer, is the same as with fractions.

Efficiency

Efficiency is work per day. If A is twice as efficient as B, A does twice as much per day and so takes half the time. Time and efficiency are inversely proportional for a fixed job.

This lets you write rates straight from a ratio. If A : B efficiency is 2 : 1, give A 2 units a day and B 1 unit a day, and let the total come from the other fact in the question.

Workers, days and hours

When each worker works at the same rate:

M₁ × D₁ × H₁ ÷ W₁ = M₂ × D₂ × H₂ ÷ W₂

M is the number of workers, D days, H hours per day and W the amount of work. If the work is the same, the W terms cancel. The rule holds because total effort is workers × days × hours, and the same job needs the same total effort.

Pipes and cisterns

A filling pipe does positive work. An emptying pipe or leak does negative work. Everything else is the same as time and work: use the LCM of the times as the tank's capacity in units.

Worked examples

Example 1. A can finish a job in 10 days and B in 15 days. How long will they take together?

1. Total work = LCM(10, 15) = 30 units. A does 3 a day, B does 2.
2. Together: 5 units a day. Time = 30 ÷ 5 = 6 days.
3. Fraction check: 1/10 + 1/15 = 3/30 + 2/30 = 1/6.

Example 2. A is twice as efficient as B. Together they finish a job in 12 days. How long would A take alone?

1. Rates: A 2 units a day, B 1. Together 3 a day.
2. Total work = 3 × 12 = 36 units.
3. A alone: 36 ÷ 2 = 18 days. (B alone would take 36 days.)

Example 3. A can do a job in 12 days and B in 18 days. They start together, but A leaves after 3 days. How long does B take to finish the rest?

1. Total = LCM(12, 18) = 36 units. A does 3 a day, B does 2.
2. In 3 days together: 3 × 5 = 15 units. Remaining: 21 units.
3. B finishes in 21 ÷ 2 = 10.5 days. The whole job takes 13.5 days.

Example 4. A can do a job in 8 days and B in 12 days. They work on alternate days, starting with A. How long does the job take?

1. Total = LCM(8, 12) = 24 units. A does 3 a day, B does 2.
2. Each two-day cycle does 5 units. Four cycles (8 days) do 20 units, leaving 4.
3. Day 9, A does 3, leaving 1. Day 10, B needs half a day for 1 unit.
4. Total: 9.5 days.

Example 5. Pipes A and B can fill a tank in 6 and 8 hours. Pipe C can empty it in 12 hours. If all three are opened together, how long will the tank take to fill?

1. Capacity = LCM(6, 8, 12) = 24 units. A fills 4 an hour, B fills 3, C empties 2.
2. Net: 4 + 3 − 2 = 5 units an hour.
3. Time = 24 ÷ 5 = 4.8 hours, which is 4 hours 48 minutes.

Example 6. 12 workers working 8 hours a day finish a job in 10 days. How many days will 16 workers take, working 5 hours a day?

1. Total effort = 12 × 8 × 10 = 960 worker-hours.
2. 16 × 5 × D = 960, so D = 12 days.

Common mistakes

• Adding days instead of rates. A in 10 days and B in 15 days do not take 25 days, or 12.5 days, together.
• In alternate-day questions, dividing total work by the two-day output and doubling without checking the last cycle.
• Treating a leak as filling rather than emptying.
• Forgetting the hours-per-day term when it changes between the two situations.

Practice

Set a 6-minute timer.

1. A takes 20 days and B takes 30 days. How long together?
2. A, B and C can do a job in 12, 18 and 36 days. How long together?
3. A is three times as efficient as B. Together they finish in 15 days. How long would A take alone?
4. Pipe A fills a tank in 8 hours; pipe B empties it in 24 hours. Both are open. How long to fill?
5. 12 people finish a job in 10 days. How long would 8 people take?
6. A and B together take 10 days; A alone takes 15 days. How long does B take alone?
7. A takes 10 days and B takes 15 days. They start together, and A leaves after 4 days. How many more days does B need?
8. 8 workers working 9 hours a day finish a job in 20 days. How many days will 12 workers take at 8 hours a day?

Answers:

1. 12 days. Total 60 units; A 3, B 2 a day; 60 ÷ 5.
2. 6 days. Total 36 units; rates 3, 2 and 1; 36 ÷ 6.
3. 20 days. Rates 3 and 1; total 4 × 15 = 60; 60 ÷ 3.
4. 12 hours. Capacity 24 units; A fills 3, B empties 1; 24 ÷ 2.
5. 15 days. 12 × 10 = 120 worker-days; 120 ÷ 8.
6. 30 days. Total 30 units; pair 3 a day, A 2 a day, so B 1 a day.
7. 5 days. Total 30 units; A 3, B 2 a day. In 4 days: 20 units. Remaining 10 ÷ 2.
8. 15 days. 8 × 9 × 20 = 1,440; 12 × 8 × D = 1,440.

What to do next

• Solve every question this week with the LCM method, even if you know the fraction method well.
• Do five alternate-day questions until the "finish day by day" step is a habit.
• Move on to speed, distance and time, which uses the same rate idea.
• See the numerical ability plan for where time and work fits in your six weeks.