Time and Work: Concepts, Formulas, and Clear Examples

If A finishes alone in $a$ days, daily work rate $=\frac{1}{a}$ of the job. Combined rate adds when working together.

MDH=W (men × days × hours = work) for same efficiency cohorts.

Efficiency ∝ $\frac{1}{\text{time}}$; more workers reduce days inversely.

Individual and combined rates

Rate

$$r = \frac{1}{T}$$

Together

$$\frac{1}{T_{\text{together}}} = \frac{1}{t_1} + \frac{1}{t_2}$$

Example — A in 10, B in 15

Together $\frac{1}{10}+\frac{1}{15}=\frac{1}{6}$ → 6 days.

Work done in partial time

Work fraction

$$\text{work} = r \times t$$

Men-days formula

MDH

$$M_1 D_1 H_1 = M_2 D_2 H_2$$

• Same work quantity; efficiency constant.

Alternate days

• Sum work per 2-day cycle; scale to full job.

Pipes link

• Filling/emptying tanks identical with sign on rate.

Negative work

• Destruction or leak subtracts rate from net completion.

Step-by-step method for exam questions

1. Express each worker rate as 1/time.
2. Add/subtract rates per stem.
3. Time = 1/net rate for full job.
4. Partial days: multiply rate × days for fraction.
5. Use MDH for workforce scaling.
6. Pick option.

Formula cheat sheet

Frequently asked questions

Different hours per day?

Include H in MDH or scale rates.

A works alone first?

Split intervals; sum work fractions to 1.

More men less days?

Inverse proportion if work fixed.

Rest days?

Count only active work days in product MD.

Practice on this platform

Use 4 practice sets (10 MCQs, detailed solution after each answer) and 2 timed mocks (20 minutes) on this topic to convert formulas into speed and accuracy.