Time and Work Cheat Sheet

Time and Work Cheat Sheet

Quick Revision

The key idea in time and work is the one-day work: if a person finishes a job in n days, then in one day they do 1/n of it.

Ready to practise? Take the Time and Work quiz

1. One-Day Work

• If A finishes a job in a days, A's one-day work = 1/a.
• If A's one-day work is 1/a, A finishes the job in a days.

2. Working Together

If A takes a days and B takes b days, then in one day together they do 1/a + 1/b, so:

Time taken together = (a × b) / (a + b)

Example

A does a job in 10 days, B in 15 days. Together:

= (10 × 15) / (10 + 15)
= 150 / 25
= 6 days

3. The LCM Method (fast)

Take the total work as the LCM of the given days; each worker's one-day work is then a whole number.

Example

A: 10 days, B: 15 days. Let total work = LCM(10, 15) = 30 units.

A's rate = 30/10 = 3 units/day
B's rate = 30/15 = 2 units/day
Together = 5 units/day → 30 / 5 = 6 days

4. Efficiency

Efficiency is inversely proportional to time.

• If A is twice as efficient as B, A takes half the time of B.
• If A : B efficiency = 2 : 1, then A : B time = 1 : 2.

5. Men–Days–Hours Relation

When the size of the workforce changes:

(M₁ × D₁ × H₁) / W₁ = (M₂ × D₂ × H₂) / W₂

where M = men, D = days, H = hours per day, W = work done.

6. Pipes and Cisterns

Pipes use the same rules, with a sign for direction:

• An inlet pipe that fills in a hours does +1/a per hour.
• An outlet (drain) pipe that empties in b hours does −1/b per hour.
• Add the rates; a positive total fills the tank, a negative total empties it.

Example

Inlet fills in 6 h, outlet empties in 8 h. Net rate = 1/6 − 1/8 = 1/24, so the tank fills in 24 hours.

7. Exam Quick Tips

• Convert every worker to a one-day (or one-hour) rate, then add.
• The LCM method avoids fractions — use it whenever days are given.
• Efficiency and time are inverse: more efficient means less time.
• In pipes, treat an outlet as negative and add the rates.

Keep revising with the rest of the Maths section:

• All Maths topics
• Time, Speed and Distance Cheat Sheet
• Ratio and Proportion Cheat Sheet

How this was made: Drafted with AI assistance; spot-checked by the editor on 31 October 2026.