Time and work for SSC GD

Time and work questions ask how long a job takes when people work alone, together, or in shifts. The fractions can get messy if you use them directly. The cleaner way is to give the job a number of units, usually the LCM of the given days, so that every step uses whole numbers.

Once you learn this one method, it covers almost every variety: workers, pipes filling tanks, someone leaving halfway, and even sharing wages. It rests on LCM and ratio, so revise those if they feel shaky.

The core idea

If a person finishes a job in n days, they do 1/n of the job each day. Two people working together add their daily work.

Two methods compared

Both give the same answer. The units method is faster in an exam because you add 3 + 2 instead of 1/10 + 1/15.

Steps for the units method

1. Take total work = LCM of all the given days (or hours).
2. Find each person's work per day: total ÷ their days.
3. Add (or subtract, for a pipe that empties) the daily work.
4. Time = work to be done ÷ work per day.

Efficiency

"A is twice as efficient as B" means A does 2 units a day for every 1 unit B does. So A takes half the time B takes. Efficiency and time are in inverse proportion.

Men, days and hours

When a job is fixed, the total effort stays the same:

M1 × D1 × H1 = M2 × D2 × H2

M is the number of workers, D the days and H the hours per day. Leave out H if the question does not mention hours.

Pipes and cisterns

A filling pipe works like a worker. An emptying pipe or a leak works against them, so subtract its units.

Sharing wages

Wages are shared in the ratio of work done. If both work the same number of days, that is the ratio of their daily work, which is the inverse of their individual times.

Solved examples

Example 1. A can finish a job in 12 days and B in 18 days. How long will they take together?

1. Total work = LCM(12, 18) = 36 units.
2. A does 36 ÷ 12 = 3 units a day; B does 36 ÷ 18 = 2.
3. Together: 5 units a day.
4. Time = 36 ÷ 5 = 7⅕ days (7.2 days).

Example 2. A, B and C can do a job in 10, 15 and 30 days respectively. How long will all three take together?

1. Total = LCM(10, 15, 30) = 30 units.
2. Daily work: A 3, B 2, C 1. Together: 6 units.
3. Time = 30 ÷ 6 = 5 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?

1. Total = LCM(20, 30) = 60 units. A does 3 a day; B does 2.
2. In 6 days together: 6 × 5 = 30 units.
3. Remaining: 60 − 30 = 30 units.
4. B alone: 30 ÷ 2 = 15 days.

Example 4. A is twice as efficient as B. Together they finish a job in 12 days. How long will A take alone?

1. Let A do 2 units a day and B 1 unit.
2. Total work = 12 × (2 + 1) = 36 units.
3. A alone: 36 ÷ 2 = 18 days. (B alone would take 36 days.)

Example 5. 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?

1. M1 × D1 × H1 = 12 × 10 × 8 = 960.
2. 20 × D2 × 6 = 960, so 120 × D2 = 960.
3. D2 = 8 days.

Example 6. Pipes A and B can fill a tank in 10 and 15 hours. Pipe C can empty it in 12 hours. If all three are opened together, how long will the tank take to fill?

1. Total = LCM(10, 15, 12) = 60 units.
2. A fills 6 an hour, B fills 4, C empties 5.
3. Net: 6 + 4 − 5 = 5 units an hour.
4. Time = 60 ÷ 5 = 12 hours.

Example 7. A can do a job in 10 days and B in 15 days. Working together, they earn ₹1,500. How should the money be shared?

1. Daily work (total 30 units): A 3, B 2.
2. They work the same days, so share in the ratio 3 : 2.
3. A gets ₹900, B gets ₹600.

Common mistakes

Practice set

1. A can finish a job in 15 days and B in 10 days. How long will they take together?
2. A and B together finish a job in 8 days. A alone takes 12 days. How long does B take alone?
3. A, B and C can do a job in 12, 15 and 20 days. How long will all three take together?
4. A is three times as efficient as B. B alone takes 24 days. How long will they take together?
5. 9 workers can build a wall in 12 days. How long will 12 workers take?
6. A can do a job in 18 days and B in 24 days. They work together for 4 days, then B leaves. How long does A take to finish the rest?
7. A pipe fills a tank in 6 hours, but a leak empties the full tank in 9 hours. With both working, how long does the tank take to fill?
8. A can do a job in 6 days and B in 12 days. Together they earn ₹1,800. Find each share.

Answers:

1. Total 30: A 2, B 3, together 5. 30 ÷ 5 = 6 days.
2. Total 24: A + B = 3, A = 2, so B = 1. B alone: 24 days.
3. Total 60: 5 + 4 + 3 = 12. 60 ÷ 12 = 5 days.
4. B does 1 unit, total 24. A does 3. Together 4 a day: 6 days.
5. 9 × 12 ÷ 12 = 9 days.
6. Total 72: A 4, B 3. In 4 days: 28 units. Remaining 44 ÷ 4 = 11 days.
7. Total 18: fill 3, leak 2, net 1. 18 hours.
8. Total 12: A 2, B 1. Ratio 2 : 1: A ₹1,200, B ₹600.

What to do next

• Solve 15 questions using only the units method.
• Practise five pipe questions with one emptying pipe.
• Learn M × D × H and try three questions where hours change.
• Move on to time and distance, which uses the same rate idea.