Time and work for RRB Group D

Time and work questions tell a small story: two people share a job, a worker leaves halfway, a leak slows a tank. Underneath, there is one idea. If someone finishes a job in n days, they do 1/n of it each day. Everything else is adding and subtracting those daily amounts.

Fractions make this slow and error-prone. The total-work method below replaces the fractions with whole numbers, and it is the method most candidates find fastest in the exam hall.

The total-work method

1. Take the total work = the LCM of the given days (or hours).
2. Find how many units each person does per day: total ÷ their days.
3. Add the daily units of people working together (subtract for anyone undoing the work).
4. Time = work ÷ units per day.

For A in 15 days and B in 10 days: total work = LCM(15, 10) = 30 units. A does 2 units a day, B does 3. Together, 5 units a day, so 30 ÷ 5 = 6 days.

If the LCM needs a refresher, see our LCM and HCF guide.

Efficiency

Efficiency is how much work someone does per day. It works the opposite way to time: if A is twice as efficient as B, A takes half the time.

• Efficiency ratio A : B = 2 : 1 means time ratio A : B = 1 : 2.
• "A is 50% more efficient than B" means efficiency 3 : 2, so time 2 : 3.

Workers, days and hours

When the same job is done by different-sized teams, the total effort stays the same:

• Workers × days = constant, or with hours: workers × days × hours = constant.
• If the amount of work also changes, divide by it: (M₁ × D₁ × H₁) ÷ W₁ = (M₂ × D₂ × H₂) ÷ W₂.

More workers means fewer days. That is inverse proportion, so the answer should always make sense: doubling the team halves the time.

Pipes and cisterns

A tank is just a job, and pipes are workers. Filling pipes add work; emptying pipes and leaks subtract it. Use the same LCM method with hours or minutes.

Worked examples

Example 1: A and B together take 8 days. A alone takes 24 days. How long does B alone take?

• Total work = LCM(8, 24) = 24 units.
• Together: 3 units a day. A: 1 unit a day. So B: 2 units a day.
• B alone = 24 ÷ 2 = 12 days.

Example 2: A is twice as efficient as B. B alone takes 30 days. How long do they take together?

• A takes half of B's time: 15 days.
• Total = 30 units. A does 2 a day, B does 1 a day, together 3.
• 30 ÷ 3 = 10 days.

Example 3: A can do a job in 20 days and B in 30 days. They work together for 6 days, then A leaves. How long does B take to finish the rest?

• Total = 60 units. A: 3 a day, B: 2 a day.
• In 6 days together: 6 × 5 = 30 units done. 30 units remain.
• B alone: 30 ÷ 2 = 15 more days.

Example 4: 12 workers working 8 hours a day finish a job in 10 days. How many days will 20 workers take working 6 hours a day?

• Total effort = 12 × 8 × 10 = 960 worker-hours.
• 20 × 6 × D = 960, so D = 8 days.

Example 5: Pipe A fills a tank in 6 hours and pipe B in 12 hours. Pipe C empties it in 8 hours. All three are open. How long does the tank take to fill?

• Total = LCM(6, 12, 8) = 24 units.
• A: +4, B: +2, C: −3 each hour. Net = 3 units an hour.
• 24 ÷ 3 = 8 hours.

Common mistakes

• Adding the days (15 + 10 = 25) instead of adding the work per day.
• Forgetting that more workers need fewer days.
• Adding a leak instead of subtracting it.
• Treating "twice as efficient" as "takes twice as long".
• In "someone leaves" questions, forgetting the work already done before they left.

Practice set

1. A takes 12 days and B takes 24 days. How long do they take together?
2. A and B together take 6 days. A alone takes 9 days. How long does B take alone?
3. 10 workers finish a job in 12 days. How many days will 8 workers take?
4. A pipe fills a tank in 5 hours; a leak empties it in 20 hours. How long does the tank take to fill with the leak open?
5. A works twice as fast as B. Together they finish a job in 10 days. How long would B take alone?
6. A, B and C can finish a job in 10, 12 and 15 days. How long do all three take together?
7. Two pipes fill a tank in 20 minutes and 30 minutes. How long do both take together?
8. A can do a job in 10 days. A works for 4 days, and B finishes the rest in 9 days. How long would B take alone?

Answers:

1. 8 days. Total 24: A 2, B 1; 24 ÷ 3.
2. 18 days. Total 18: together 3, A 2, so B 1; 18 ÷ 1.
3. 15 days. 10 × 12 = 8 × D.
4. 6 hours 40 minutes. Total 20: fill +4, leak −1, net 3; 20 ÷ 3 = 6⅔ hours.
5. 30 days. Efficiency 2 : 1, together 3 units a day for 10 days = 30 units; B does 1 a day.
6. 4 days. Total 60: 6 + 5 + 4 = 15 a day; 60 ÷ 15.
7. 12 minutes. Total 60: 3 + 2 = 5 a minute; 60 ÷ 5.
8. 15 days. A does 4/10 = 2/5 in 4 days; B does the other 3/5 in 9 days, so the whole job takes 9 ÷ 3/5 = 15 days.

What to do next

• Solve ten two-person questions with the LCM method, never with fractions.
• Practise three "someone leaves midway" questions and three pipe-and-leak questions.
• Learn the efficiency–time rule: double the efficiency, half the time.
• Go on to time, speed and distance, which uses the same "rate × time" thinking.