Time and Work Notes for SSC Exams

Time and Work is one of the most important chapters of SSC Quantitative Aptitude. Two to three questions come from it in each Tier 1 paper, and pipes and cisterns uses the same logic. These time and work notes for SSC explain the basic idea, the fast LCM method and the standard formulas with examples and practice questions.

The Basic Idea of Time and Work

Work done is always compared with time taken. If a person can finish a job in x days, then his one-day work is 1/x of the job.

• Work = Rate x Time.
• If A can do a job in x days, then A's one-day work = 1/x.
• If A and B can do a job in x and y days, then together they take x y / (x + y) days.
• More men means fewer days (inverse proportion), and more work means more days (direct proportion).

Important Time and Work Formulas

The LCM Method (Fastest Way)

Take the total work as the LCM of the days of all workers. Then the work done per day (efficiency) of each worker is total work divided by his days. This avoids fractions and makes every question easy.

• A takes 10 days and B takes 15 days. LCM = 30 units of work.
• A's efficiency = 30 / 10 = 3 units per day. B's efficiency = 30 / 15 = 2 units per day.
• Together they do 5 units a day, so the job takes 30 / 5 = 6 days.

Wages and Alternate Days

Wages are divided in the ratio of the work done by each person. If A and B work for different numbers of days, multiply efficiency by days for each person. In alternate-day questions (A works on day 1, B on day 2, and so on), find the work done in two days, then use it to find the total time.

Leaving and Joining the Work

If a worker leaves before the work ends, assume the total time as x days and write an equation of the work done by each person. Remember that the person who stayed for the whole time works x days, and the person who left earlier works fewer days.

Solved Examples

Example 1: A can do a job in 12 days and B in 18 days. In how many days will they finish it together?
Solution: Together = 12 x 18 / (12 + 18) = 216 / 30 = 7.2 days.

Example 2: A can do a piece of work in 10 days and B in 15 days. Using the LCM method, find the time taken together.
Solution: LCM = 30. A = 3 units a day, B = 2 units a day. Together = 5 units a day. Time = 30 / 5 = 6 days.

Example 3: A and B together can finish a job in 12 days. A alone can finish it in 20 days. How long will B take alone?
Solution: B's one-day work = 1/12 - 1/20 = (5 - 3) / 60 = 1/30. So B takes 30 days.

Example 4: 12 men can complete a work in 15 days. How many days will 9 men take?
Solution: Total work = 12 x 15 = 180 man-days. Days for 9 men = 180 / 9 = 20 days.

Example 5: A can finish a work in 20 days and B in 30 days. They start together, but A leaves 5 days before the work is finished. In how many days is the work finished?
Solution: Let the total time be x days. B works x days and A works (x - 5) days. x/30 + (x - 5)/20 = 1, so 2x + 3(x - 5) = 60, 5x = 75 and x = 15 days.

Example 6: Rs 1,200 is to be paid to A, B and C, who can finish a job in 10, 15 and 30 days respectively. They all work together. Find the share of each.
Solution: LCM = 30. Efficiencies are 3, 2 and 1. Shares are in the ratio 3 : 2 : 1, so they get Rs 600, Rs 400 and Rs 200.

Quick Tips to Solve Faster

• Always use the LCM method to avoid fractions.
• Efficiency is inversely proportional to the time taken.
• For wages, divide in the ratio of the total work done by each person.
• In "leaves the work" problems, define the total time as x and write one equation.
• Use M1D1 = M2D2 when the work and hours are the same.

Common Mistakes to Avoid

• Adding the days instead of adding the one-day work.
• Forgetting that a person who leaves earlier has worked fewer days.
• Dividing wages in the ratio of days instead of the work done.
• Mixing the men-days relation when the hours per day also change.
• Not checking whether the answer is in days or in hours.

Quick Revision Points

• One-day work = 1 / number of days.
• A and B together = xy / (x + y).
• LCM of days = total work; total work / days = efficiency.
• Wages are in the ratio of work done.
• Men x days x hours is proportional to work.

Practice Questions With Answers

1. A can do a work in 15 days and B in 10 days. In how many days will they finish it together?
   Answer: 6 days (15 x 10 / 25).
2. A and B together can finish a job in 8 days. A alone takes 12 days. How long will B alone take?
   Answer: 24 days (1/8 - 1/12 = 1/24).
3. A is twice as efficient as B, and together they finish a job in 12 days. How long will A alone take?
   Answer: 18 days (A = 2, B = 1, total work = 36).
4. 8 men can do a work in 12 days. How many days will 6 men take?
   Answer: 16 days (96 / 6).
5. A, B and C can do a work in 9, 18 and 6 days. In how many days will they finish it together?
   Answer: 3 days (1/9 + 1/18 + 1/6 = 1/3).
6. A can finish a job in 12 days. He works for 4 days and then leaves. B finishes the rest in 4 days. How long will B take alone?
   Answer: 6 days (Remaining work = 2/3).
7. Rs 900 is paid to A and B, where A is twice as efficient as B and both work for the same time. How much does A get?
   Answer: Rs 600 (Ratio 2 : 1).
8. 10 men finish a work in 24 days. How many men are needed to finish it in 16 days?
   Answer: 15 men (240 / 16).
9. A and B work on alternate days starting with A. A alone takes 10 days and B alone takes 15 days. In how many days is the work finished?
   Answer: 12 days (Total 30 units, 3 + 2 = 5 in 2 days).
10. A alone can do a job in 24 days and B alone in 40 days. In how many days will they finish it together?
    Answer: 15 days (24 x 40 / 64).

How to Practise This Chapter

1. Learn the formulas in the table until you can write them without looking.
2. Solve the solved examples again on your own, without reading the solution.
3. Attempt the practice questions above with a timer of 10 minutes.
4. Solve the matching SSC pipes and cisterns practice paper to test yourself in exam style.
5. Check the previous year papers to see how SSC frames this topic.

Related Notes and Practice Papers

• Ratio and Proportion Notes
• Average Notes
• Speed, Distance and Time Notes
• Percentage Notes
• SSC Pipes and Cisterns Practice Paper

Explore More SSC Subjects

SSC exams test many subjects, so connect this topic with the related subjects below:

• Reasoning Notes
• Statistics Notes
• Indian Economy Notes
• English Notes
• General Awareness Notes
• All SSC subjects and notes

Frequently Asked Questions

What is time and work in simple words?

Time and work is the study of how long different persons or machines take to complete a job, working alone or together.

How many questions come from time and work in SSC exams?

Two to three questions come from time and work in SSC CGL and CHSL Tier 1, apart from pipes and cisterns.

What is the formula for two persons working together?

If A takes x days and B takes y days, they take xy / (x + y) days together.

What is the LCM method in time and work?

Take the LCM of the days as the total work. Then the work done per day by each person is the total work divided by his days.

How are wages divided in time and work?

Wages are divided in the ratio of the work done by each person, which is efficiency multiplied by the days worked.

What is efficiency?

Efficiency is the amount of work done in one day. It is inversely proportional to the number of days taken.

How do I solve questions where a person leaves in the middle?

Assume the total time as x, write the work done by each person using his working days, and equate the sum to 1 (or the total work).

Is pipes and cisterns the same as time and work?

Yes. Inlet pipes behave like workers and outlet pipes behave like negative workers, so the same method is used.

How should I practise time and work?

Use the LCM method on every question, solve the examples here and then attempt the practice paper and previous year questions.