Time & work

Time & Work – Quick & Easy Study Notes

For beginners in Quantitative Aptitude – no jargon, just plain language.

1. What is “Time & Work”?

• Time: How long it takes to finish a job.
• Work: The whole job that needs to be finished (e.g., painting a wall, filling a tub).

Think of time as the clock and work as the whole cake you want to bake.

2. How do we talk about “how fast” someone works?

• Instead of “rate,” we say speed of work.
• Speed of work = How much of the job one person finishes in one hour.

Example
Alice can paint an entire wall in 4 hours.
Her speed = 1 wall ÷ 4 hours = 0.25 wall per hour.

3. “Work Done” – the part of the job finished

• If someone works for a certain time, work done = speed × time.
• Work is measured in “whole jobs” (or fractions of a job).

Example
Bob paints at 0.20 wall/hour.
In 3 hours he does 0.20 × 3 = 0.6 wall.

4. One person, one job

Formula
[ T = \frac{W}{S} ]

Tiny Example
If a machine needs 8 hours to fill a tank, its speed = 1 tank ÷ 8 h = 0.125 tank/h.
So (T = \frac{1}{0.125} = 8) hours – matches the story.

5. Two or more people working together

When people work together, you add their speeds.

Example

• Alice: 0.25 wall/hour
• Bob: 0.20 wall/hour
  Combined speed = 0.25 + 0.20 = 0.45 wall/hour
  If they paint together, the wall will be finished in
  [ T = \frac{1}{0.45} \approx 2.22\text{ hours} ]

6. Partial work – working for only part of the job

• Work done in a given time = speed × time.
• If they stop early, the remaining work is the difference.

Example
Alice and Bob together (speed 0.45 wall/h) work for 1 hour.
Work done = 0.45 × 1 = 0.45 wall.
Remaining wall = 1 – 0.45 = 0.55 wall.

7. Changing the number of workers

Adding or removing workers changes the combined speed linearly.

Example
5 workers each paint 0.10 wall/h → combined speed 0.50 wall/h.
If 2 workers leave, 3 workers remain → speed 0.30 wall/h.
Time to finish a wall: (T = 1 ÷ 0.30 \approx 3.33) hours.

8. One worker replaces another

If worker A leaves and worker B takes their place:

• New combined speed = (speed of all other workers) + speed of B.
• Use the same “speed × time” idea.

Tiny Example
4 workers paint a wall in 4 hours (speed 0.25 wall/h each).
One leaves; a faster worker B can paint at 0.40 wall/h.
New speed = 3×0.25 + 0.40 = 1.15 wall/h.
New time = (1 ÷ 1.15 \approx 0.87) hours.

9. Tips for Solving Problems

1. Identify the job (usually 1 whole job).
2. Translate words into speed (jobs per hour).
3. Add speeds when people work together.
4. Use “speed × time = work” to find missing pieces.
5. Check units: keep everything in “jobs” and “hours”.

10. Mini‑Practice Question

Three painters can paint a wall in 6 hours. One of them is replaced by a faster painter who would finish the wall in 4 hours if he worked alone. How long will it take the new team of three to paint the wall?

Solution Outline

1. Find each original painter’s speed: (1 ÷ 6 = 0.1667) wall/h.
2. Fast painter’s speed: (1 ÷ 4 = 0.25) wall/h.
3. New combined speed: (2 × 0.1667 + 0.25 = 0.5834) wall/h.
4. New time: (1 ÷ 0.5834 ≈ 1.71) hours.

11. Quick Recap