SSC CGL Maths · Time and Work

Working on Alternate Days

When workers take turns, find the work done in one full cycle of turns, count how many whole cycles fit, then finish the last part one day at a time.

All Time and Work notes

Why this matters

Nineteen questions in the bank, sixteen of them MODERATE and one HARD: two people on alternate days, three in rotation, or helpers who join every second, third or fifth day. Nearly every wrong option comes from the last cycle, so this page always finishes it one day at a time.

Concept 1 of 2: Taking turns on alternate days

Two days of turns make one cycle, and every cycle does the same amount of work. Fill the job cycle by cycle until less than a cycle is left, then go day by day, starting with whoever's turn it is.

Definition

Take the job as LCM units. One cycle does the sum of the turn-takers' daily units.
Whole cycles: take as many as fit while some work is still left after them. Then go day by day in the same order. The last day may be a part day: units left $\div$ that worker's daily units.
Who starts matters when the job ends inside a cycle. With the faster worker first, it can end sooner.
The job is a whole number of cycles: the answer is cycles $\times$ cycle length, but check the first worker of the last cycle cannot already finish it.
Three people in rotation: the cycle is 3 days, and the same steps apply.

Worked example

A can finish a job in 6 days and B in 15 days. They work on alternate days, A starting. In how many days is the job done?

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2023 · Tier I, 21 Jul 2023, Shift 4 · Q56Moderate

Example 1 · Time and Work · Working on Alternate Days

A can do a piece of work in 8 days, while B can do it in 18 days. In how many days will the work be completed if they both work on alternate days starting with B?

Rounding a part day up to a whole day

After the last whole cycle, work day by day. If 3 units are left and it is the turn of a worker who does 4 units a day, the last day is

\frac{3}{4}

of a day.

Ignoring who starts

When the job ends inside a cycle, the starter matters. A 6-day worker and a 15-day worker on alternate days finish in

8\frac{2}{5}

days if the faster one starts and in 9 days if the slower one starts.

Taking one cycle too many

Count whole cycles only while work remains after them. A 30-unit job with a 7-unit cycle takes 4 whole cycles (28 units) and then single days, not 5 cycles (35 units).

Drill 12 more on taking turns on alternate days

Concept 2 of 2: Helpers who join every few days

One person works every day and others join on a fixed rhythm. Treat the rhythm as a block of days: the regular worker's days plus the helpers' one day.

Definition

Helpers every $k$ -th day: one block is $k$ days. Its work $=$ the regular worker's $k$ days $+$ the helpers' work on their day.
Fill whole blocks, then go day by day. The helpers' day is the LAST day of each block, so in a part block at the end they may not appear at all.
Days off: a worker who rests after every 4 days of work rests on days 5, 10, 15 and so on. By day $n$ he has worked $n - \lfloor n/5 \rfloor$ days ( $\lfloor x \rfloor$ means $x$ with its fraction dropped).
One works daily, two alternate: if R works every day while S and T take turns, the cycle is 2 days: R and T, then R and S.

Worked example

A can finish a job in 16 days, B in 24 days and C in 48 days. A works every day, and B and C both help him on every fourth day. In how many days is the job done?

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 12 Sep 2025, Shift 2 · Q62Moderate

Example 2 · Time and Work · Working on Alternate Days

A, B, and C are capable of completing a job in 30, 45, and 90 days, respectively. A works every day, while B and C join A every fifth day. How long will it take to finish the task?

Putting the helpers' day first

Helpers who join on every third day work on days 3, 6, 9 and so on, not on days 1, 4, 7. In a part block at the end they may never appear.

Reading a day off after every 4 days as a 4-day rhythm

A worker who takes a day off after every four days of work is off on days 5, 10, 15: the rhythm is 5 days long, 4 working and 1 off.

Drill 5 more on helpers who join every few days

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.

Watch out for (5)

Rounding a part day up to a whole day
→ Taking turns on alternate days
Ignoring who starts
→ Taking turns on alternate days
Taking one cycle too many
→ Taking turns on alternate days
Putting the helpers' day first
→ Helpers who join every few days
Reading a day off after every 4 days as a 4-day rhythm
→ Helpers who join every few days

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 19 questions