SSC CGL Maths · Time and Work

Men, Women and Equivalent Workers

When men, women and boys work at different rates, turn every worker into one common unit, such as woman-days, and the question becomes a man-days question.

All Time and Work notes

Why this matters

Twenty-two questions in the bank, sixteen of them MODERATE: "1 man or 2 women", two mixed teams doing the same job, or a team's time with one worker's time given. Find how many women one man is worth, and the rest is a single division.

Concept 1 of 3: Whole teams working together

A team that finishes a job in 6 days does a sixth of it each day, exactly like one worker who needs 6 days. Two teams on the same job add their rates.

Definition

Treat each named team as one worker: team rate $= 1 \div$ the team's days.
Two teams together: add the rates, or use product over sum of the two times.
"Team A or team B in $d$ days": the two teams have the same rate, so together they take $\frac{d}{2}$ days.

Worked example

12 men can lay a road in 18 days, and 20 women can lay it in 9 days. If all of them work together, how many days do they take?

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 21 Sep 2025, Shift 2 · Q62Easy

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

A group of 5 men or 12 women can complete a task in 70 days. Find the time taken by 5 men and 12 women to complete the task.

Averaging the two teams' times

Two teams that take 12 and 24 days alone take 8 days together, not 18. Teams combine like single workers: add the rates.

Drill 3 more on whole teams working together

Concept 2 of 3: Converting men into women

If 8 men or 12 women do the same job in the same time, then 8 men do the work of 12 women, and one man is worth 1.5 women. Swap every man for 1.5 women and you have an all-women team, which is a man-days question.

Definition

Same job, same time: $a$ men $= b$ women, so 1 man $= \frac{b}{a}$ women.
Same job, different times: compare labour. $a$ men in $d_1$ days and $b$ women in $d_2$ days give $a d_1$ man-days $= b d_2$ woman-days.
Then turn the team in the question into women, find the job in woman-days, and divide.
Three kinds of worker, fast route: if 1 man = 2 women = 3 boys, give them daily units from the LCM: a man 6, a woman 3 and a boy 2.
A team that changes partway: take the labour already done off the total and divide the rest by the new team, as with men added partway.

Equivalent workers

a \, d_1 \text{ man-days} = b \, d_2 \text{ woman-days} \qquad 1 \text{ man} = \frac{b \, d_2}{a \, d_1} \text{ women}

amen in the first team
bwomen in the second team
$d_1, d_2$ days each team takes

Worked example

6 men can do a job in 20 days and 10 women can do it in 18 days. How many days will 4 men and 6 women take working together?

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 23 Sep 2025, Shift 2 · Q65Moderate

Example 2 · Time and Work · Men, Women and Equivalent Workers

If 10 men or 15 women can complete a work in 170 days, how long will 20 men and 20 women take for completing the same work?

Setting men equal to women without the days

8 men in 10 days and 10 women in 12 days do not make 8 men equal to 10 women. Compare labour: 80 man-days

= 120

woman-days, so 1 man

= 1.5

women.

Converting the wrong way

If 1 man

= 1.5

women, then 4 men

= 6

women and 1 woman

= \frac{2}{3}

of a man. Multiply when going from men to women, and divide when going back.

Drill 7 more on converting men into women

Concept 3 of 3: Two mixed teams doing the same job

Two mixed teams finish the same job, so the labour they put in is equal. Writing that as an equation in one man's and one woman's daily work tells you how many women a man is worth.

Definition

Team 1 has $x_1$ men and $y_1$ women and takes $d_1$ days; team 2 takes $d_2$ days. Same job: $d_1(x_1 m + y_1 w) = d_2(x_2 m + y_2 w)$ .
Solve for $m$ in terms of $w$ . The job is then $d_1(x_1 m + y_1 w)$ , written in woman-days.
Same days: if both teams take the same number of days, set the two teams equal directly.
One worker's time given: if one woman alone would take a known time, the women's share of the team's daily work is known, and the rest is the men's.
Earnings instead of days: divide each team's pay by its days to get daily pay, then solve the two equations for one man's (or woman's, or boy's) daily pay.

Two mixed teams

d_1(x_1 m + y_1 w) = d_2(x_2 m + y_2 w)

$x_1, x_2$ men in each team
$y_1, y_2$ women in each team
$d_1, d_2$ days each team takes
m, wone man's and one woman's daily work

Worked example

3 men and 4 women can finish a job in 11 days, while 2 men and 7 women can finish it in 10 days. How many days will 5 women take?

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 20 Sep 2025, Shift 1 · Q63Moderate

Example 3 · Time and Work · Men, Women and Equivalent Workers

6 women and 4 men can complete a work in 10 days, while 4 women and 5 men complete it in 10 days. In how many days will 8 women complete it?

Setting the teams equal when the days differ

If the two teams take different numbers of days, multiply each team by its days before setting them equal. Only when the days are the same can the teams be set equal directly.

Not checking with the second team

After finding

m

in terms of

w

, work out the job in woman-days from both teams. If the two totals differ, the ratio is wrong.

Drill 9 more on two mixed teams doing the same job

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 (2)

Converting men into women
Equivalent workers
$a \, d_1 \text{ man-days} = b \, d_2 \text{ woman-days} \qquad 1 \text{ man} = \frac{b \, d_2}{a \, d_1} \text{ women}$
Two mixed teams doing the same job
Two mixed teams
$d_1(x_1 m + y_1 w) = d_2(x_2 m + y_2 w)$

Watch out for (5)

Averaging the two teams' times
→ Whole teams working together
Setting men equal to women without the days
→ Converting men into women
Converting the wrong way
→ Converting men into women
Setting the teams equal when the days differ
→ Two mixed teams doing the same job
Not checking with the second team
→ Two mixed teams doing the same job

Test yourself on Time and Work

20 past SSC CGL questions from this chapter, timed at 12 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 22 questions