CDS Mathematics · Time and Work

Men, Women and Equivalent Workers

When a gang mixes kinds of worker, first find each kind's daily rate (or how many of one equal one of the other), then add the gang's rates.

All Time and Work notes CDS Mathematics strategy

Why this matters

Nine PYQs, none HARD. Two patterns: '12 men OR 18 women in 14 days' gives each rate directly; '6 men AND 8 women in 10 days, 13 men and 24 women in 4 days' gives an equation that fixes how many women equal one man.

Concept 1 of 1: Rates of different workers

'Or' gives each kind a rate on its own. 'And' twice over gives two gangs that do the same job, so their rate-times-days are equal — one equation that relates a man's rate to a woman's.

Definition

' $m$ men OR $w$ women in $d$ days': a man does $\dfrac1{md}$ , a woman $\dfrac1{wd}$ a day.
Two mixed gangs, days $d_1$ and $d_2$ : $d_1(a_1M + b_1W) = d_2(a_2M + b_2W)$ gives $M : W$ .
Once $M : W$ is known, turn every gang into one kind and use man-days.
A gang that is each group together finishes in half the time.

Two gangs, same job

d_1(a_1M + b_1W) = d_2(a_2M + b_2W)

Worked example

9

men or

15

women can do a job in

20

days. How long do

6

men and

5

women take?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2017 · CDS (I) 2017 — Elementary Mathematics · Q30Moderate

Example 1 · Time and Work · Men, Women and Equivalent Workers

If 5 men can do a piece of work in 10 days and 12 women can do the same work in 15 days, the number of days required to complete the work by 5 men and 6 women is

OR is not AND

8

men or

12

women in

24

days' means each group ALONE takes

24

days. Together they take

12

, not

24

Drill 8 more on rates of different workers

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)

Rates of different workers
Two gangs, same job
$d_1(a_1M + b_1W) = d_2(a_2M + b_2W)$

Watch out for (1)

OR is not AND
→ Rates of different workers

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 test Drill all 9 questions