PYQ Vault

CDS Mathematics · Time and Work

Man-Days and Man-Hours

A fixed job needs a fixed number of man-days (or man-hours), so men × days × hours stays constant for the same work.

All Time and Work notesCDS Mathematics strategy

Why this matters

Seventeen PYQs, none HARD. Extra men to finish on time, men who leave half-way, a bigger wall, 20 persons and 20 floors: measure the job in man-days once, then share out what is left. Five more hide the same idea inside algebra, 'work of (x + 2) men in (x − 3) days'.

Concept 1 of 1: Men × days × hours

Twice the men finish in half the days; twice the work needs twice the man-days. So M1D1H1W1=M2D2H2W2\dfrac{M_1D_1H_1}{W_1} = \dfrac{M_2D_2H_2}{W_2} for any two gangs of equal workers.

Definition

  • M1D1H1W1=M2D2H2W2\dfrac{M_1 D_1 H_1}{W_1} = \dfrac{M_2 D_2 H_2}{W_2}.
  • Part done, part left: total man-days == man-days used ÷\div fraction done; the rest is shared over the days left.
  • Men leaving in batches: add the man-days block by block until the job is covered.
  • Work measured by size (a wall's volume, rooms, hectares): the work is proportional to it.

Constant work

M1D1H1W1=M2D2H2W2\dfrac{M_1 D_1 H_1}{W_1} = \dfrac{M_2 D_2 H_2}{W_2}

Worked example

1616 men working 66 hours a day finish a job in 1515 days. How many days do 1212 men working 88 hours a day need?
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2018 · CDS (II) 2018 — Elementary Mathematics · Q40Easy

Example 1 · Time and Work · Man-Days and Man-Hours

Twelve (12) men work 8 hours per day and require 10 days to build a wall. If 8 men are available, how many hours per day must they work to finish the work in 8 days ?

Count the whole job, not the part

If a quarter took 10,00010{,}000 man-days, the job is 40,00040{,}000 and the part LEFT is 30,00030{,}000. Sharing 40,00040{,}000 over the days left overstates the men needed.

Additional men, or men in all?

The calculation gives the number of men who must be working. Subtract the men already there when the question asks for ADDITIONAL men.
Drill 16 more on men × days × hours

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

  • Men × days × hours

    Constant work

    M1D1H1W1=M2D2H2W2\dfrac{M_1 D_1 H_1}{W_1} = \dfrac{M_2 D_2 H_2}{W_2}

Watch out for (2)

Test yourself on Time and Work

15 past CDS questions from this chapter, timed at 18 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Take the Time and Work chapter testDrill all 17 questions