Time and Work Tricks: LCM Method, Pipes and Cisterns and Wages Questions for SSC CGL, CHSL

Time and work and pipes and cisterns are favourite topics of SSC CGL and CHSL maths. A work or a tank is done at a certain rate, and you find the time, the efficiency or the wages. The LCM method removes the fractions and makes these questions simple. These time and work tricks for SSC explain the method with solved questions of every type.

Basic Idea

• If a person does a work in n days, he does 1/n of the work in one day.
• Work = Efficiency × Time.
• If A does a work in x days and B in y days, together they take xy/(x + y) days.

LCM (Efficiency) Method

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

Other Rules

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) = 7.2 days.

Example 2 (LCM method). 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 = 30 units. Efficiencies: 3, 2 and 1. Together = 6. Time = 30/6 = 5 days.

Example 3. A and B together do a work in 12 days. A alone does it in 20 days. In how many days can B alone do it?
1/12 − 1/20 = 1/30. So B takes 30 days.

Example 4 (joining later). A can do a work in 10 days and B in 15 days. A starts and B joins after 2 days. In how many days is the work done?
In 2 days A does 2/10 = 1/5. The remaining 4/5 is done at the rate 1/10 + 1/15 = 1/6 a day, which takes 4.8 days. The total = 2 + 4.8 = 6.8 days.

Example 5. 15 men can do a work in 20 days. In how many days can 25 men do it?
15 × 20 = 25 × D, so D = 12 days.

Example 6 (wages). A, B and C have the efficiencies 1 : 2 : 3 and work for the same number of days. They earn 1,200 rupees in all. Find the share of each.
Shares = 200, 400 and 600 rupees.

Example 7 (pipes). A pipe fills a tank in 20 minutes and another pipe in 30 minutes. In how many minutes do both fill it?
20 × 30/50 = 12 minutes.

Example 8 (alternate days). A can do a work in 10 days and B in 15 days. They work on alternate days, starting with A. When is the work finished?
In 2 days they do 1/10 + 1/15 = 1/6. So 6 cycles are needed, which is 12 days.

Quick Tips

• Use the LCM method as the default.
• For wages, use efficiency × days.
• Treat a leak as a negative pipe.
• For alternate days, find the work of 2 days first.

Quick Revision Points

• One-day work = 1/n.
• Together = xy/(x + y) days.
• Total work = LCM of the days.
• M1D1/W1 = M2D2/W2.
• Wages are in the ratio of the work done.

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 does a work in 20 days. How much work does he do in 5 days?
   Answer: 1/4
3. A is twice as efficient as B. A alone takes 12 days. How many days does B take?
   Answer: 24 days
4. 10 men do a work in 12 days. In how many days will 15 men do it?
   Answer: 8 days
5. A takes 6 days and B takes 12 days to do a work. In how many days together?
   Answer: 4 days
6. A pipe fills a tank in 15 minutes and another in 10 minutes. In how many minutes together?
   Answer: 6 minutes
7. An inlet fills a tank in 4 hours and an outlet empties it in 6 hours. In how many hours does the tank fill with both open?
   Answer: 12 hours
8. A, B and C have efficiency 3 : 2 : 1 and they earn 1,800 rupees for equal days. Find A’s share.
   Answer: 900 rupees
9. A can do a work in 8 days. He works for 3 days. How much work is left?
   Answer: 5/8
10. 12 men do a work in 15 days. In how many days will 18 men do it?
    Answer: 10 days

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Mathematics notes page, read the previous topic Ratio, Proportion and Alligation and the next topic Time, Speed and Distance Tricks. Formulas are in the Formula Guide and more practice is in the Quantitative Aptitude notes. Also read the Time and Work Formula Guide.

Frequently Asked Questions

What is the formula of time and work?

If a person takes n days, his one-day work is 1/n, and the work is efficiency times time.

What is the LCM method?

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.

How do I find the time taken by two persons together?

xy divided by (x + y) days.

What is the men-days formula?

M1 × D1 / W1 = M2 × D2 / W2.

How are wages divided?

In the ratio of the work done, which is efficiency times the days.

How do I solve a leak question?

Subtract the work of the leak from the work of the inlet pipe.

What if a person leaves in the middle?

Find the work done till he leaves, and the remaining work by the others.

What is alternate days work?

Two persons work on alternate days, and you find the work of two days first.

Is time and work asked in SSC exams?

Yes. It is asked in every SSC maths paper.

What are common mistakes?

Not using the same unit of time, and forgetting the work that is done before a person joins.

How much time should I take?

About 40 to 60 seconds.

What is efficiency?

It is the amount of work done in one unit of time.