Time and Work, Pipes and Cisterns Formula Guide for SSC Exams

Time and work questions look different from pipes and cisterns questions, but the idea is the same: a work (or a tank) is done at a certain rate. This time and work, pipes and cisterns formula guide for SSC gives the formulas of the one-day work, the LCM (efficiency) method, the wages, the men-days formula and the pipes and leak formulas, with solved examples.

Basic Formulas of Time and Work

LCM (Efficiency) Method

1. Take the total work as the LCM of the days taken by all the persons.
2. Efficiency of each person = Total work / Days taken by that person.
3. Add the efficiencies of the persons who work together.
4. Time taken = Total work / Combined efficiency.

Men, Days and Hours

For the same kind of work, M1 × D1 × H1 / W1 = M2 × D2 × H2 / W2, where M is the number of men, D the number of days, H the hours per day and W the amount of work. If the work is the same, M1 × D1 = M2 × D2 when the hours are the same.

Wages

• Wages are divided in the ratio of the work done by each person.
• Work done = Efficiency × Number of days.
• If all the persons work for the same number of days, the wages are divided in the ratio of their efficiencies.

Alternate Days

If A and B work on alternate days, find the work done in two days (one day of A and one day of B) and then the number of such cycles that are needed.

Pipes and Cisterns

The inlet pipes are counted as positive and the outlet pipes are counted as negative.

Solved Examples

Example 1. A can do a work in 12 days and B in 18 days. In how many days can they do it together?
(12 × 18) / (12 + 18) = 216 / 30 = 7.2 days.

Example 2. A, B and C can do a work in 10, 15 and 30 days. In how many days will they finish it together?
Total work = LCM = 30 units. The efficiencies are 3, 2 and 1. The combined efficiency is 6, so the time is 30 / 6 = 5 days.

Example 3. 12 men can do a work in 15 days. How many men are needed to do it in 10 days?
12 × 15 = M × 10, so M = 18 men.

Example 4. A and B together earn 900 rupees for a work. A is twice as efficient as B and both work for the same number of days. Find the share of each.
The ratio is 2 : 1, so A gets 600 rupees and B gets 300 rupees.

Example 5. A pipe fills a tank in 6 hours, but a leak empties it in 12 hours. How long will the tank take to fill with the leak?
(1/6 − 1/12) = 1/12 per hour, so the time is 12 hours.

Example 6. A can do a work in 10 days and B in 15 days. They work on alternate days, starting with A. In how many days is the work finished?
In 2 days they do 1/10 + 1/15 = 1/6 of the work. So 6 such cycles are needed, which is 6 × 2 = 12 days.

Quick Tips

• Use the LCM method as the default, because it avoids fractions.
• In wage questions, find the work of each person as efficiency times days.
• Treat the leak as a negative pipe.
• Check that the units of time (days, hours, minutes) are the same throughout the question.

Quick Revision Points

• A person who takes n days does 1/n of the work in one day.
• Two persons take xy/(x + y) days together.
• Total work = LCM of the days in the LCM method.
• M1D1/W1 = M2D2/W2.
• An outlet pipe or leak is counted as negative work.

Practice Questions With Answers

1. A can do a work in 10 days and B in 15 days. In how many days will they do it together?
   Answer: 6 days
2. A can do a work in 20 days. How much work does A do in 5 days?
   Answer: 1/4 of the work
3. A is twice as efficient as B. A alone takes 12 days. How many days does B take alone?
   Answer: 24 days
4. 10 men can do a work in 12 days. How many days will 15 men take?
   Answer: 8 days
5. A takes 6 days and B takes 12 days to do a work. In how many days will they do it together?
   Answer: 4 days
6. One pipe fills a tank in 15 minutes and another in 10 minutes. In how many minutes will they fill it together?
   Answer: 6 minutes
7. A pipe fills a tank in 4 hours and another pipe empties it in 6 hours. In how many hours will the tank fill if both are open?
   Answer: 12 hours
8. A and B work for 6 days and 4 days with the same efficiency. They earn 1000 rupees. Find the share of A.
   Answer: 600 rupees
9. A can do a work in 8 days and works for 3 days. How much work is left?
   Answer: 5/8 of the work
10. Write the formula for men, days and work.
    Answer: M1 × D1 / W1 = M2 × D2 / W2

How to Practise This Chapter

Write each formula on a card, with a solved example on the back, and revise the cards every day. Then test yourself with our practice papers and the previous year papers page. See all guides on the Formula Guide page, and also read the Mathematics notes and Quantitative Aptitude notes. The previous guide is Time, Speed and Distance and the first guide is Arithmetic.

Frequently Asked Questions

What is the formula for the work done in one day?

If a person takes n days to do a work, the work done in one day is 1/n.

What is the formula for two persons working together?

They take xy divided by (x + y) days, where x and y are the days taken alone.

What is the LCM method of time and work?

Take the total work as the LCM of the days, find the efficiency of each person, and divide the total work by the combined efficiency.

What is the men-days formula?

M1 times D1 divided by W1 equals M2 times D2 divided by W2.

How are the wages divided between the workers?

They are divided in the ratio of the work done, which is efficiency times days.

What is a pipe in the cistern problems?

An inlet pipe fills the tank, and an outlet pipe or a leak empties it.

How do I solve a problem with a leak?

Subtract the work of the leak from the work of the inlet pipe, and then find the time.

What if two persons work on alternate days?

Find the work of the two days together, find the number of cycles and then add the extra days if needed.

If A is twice as efficient as B, what is the ratio of the days?

The ratio of the days is 1 : 2, because the more efficient person takes less time.

What is the relation between efficiency and time?

Efficiency is inversely proportional to the time for the same work.

Is this topic asked in SSC exams?

Yes. Time and work, and pipes and cisterns questions are asked in every SSC maths paper.

How many questions come from this topic in SSC exams?

Usually two to four questions, but the number changes from exam to exam.