ABHYAS PREP: COMMERCIAL ARITHMETIC · TIME & WORK

Two people working on alternate days

Take total work as the LCM of the days. Count full two-day cycles, then see who finishes the remainder on the last day.

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Worked examples

Example 1 · level 1

A can do a piece of work in 10 days and B in 12 days. They work on alternate days, A starting. In how many days is the work finished?

10 5/6 days
5 5/11 days
10 10/11 days
11 days

Show solution

Total work = 60 units; A = 6/day, B = 5/day; a two-day cycle = 11 units.
5 full cycles (10 days) do 55 units, leaving 5.
A works next and the rest is finished on the following day(s): total 10 5/6 days.

Answer: 10 5/6 days

Example 2 · level 2

A can do a piece of work in 14 days and B in 21 days. They work on alternate days, A starting. In how many days is the work finished?

17 days
16 4/5 days
16 2/3 days
8 2/5 days

Show solution

Total work = 42 units; A = 3/day, B = 2/day; a two-day cycle = 5 units.
8 full cycles (16 days) do 40 units, leaving 2.
A works next and the rest is finished on the following day(s): total 16 2/3 days.

Answer: 16 2/3 days

Example 3 · level 3

A can do a piece of work in 6 days and B in 12 days. They work on alternate days, B starting. In how many days is the work finished?

10 days
4 days
9 days
8 days

Show solution

Total work = 12 units; A = 2/day, B = 1/day; a two-day cycle = 3 units.
4 full cycles (8 days) do 12 units, leaving 0.
Nothing is left, so the work ends after 8 days.

Answer: 8 days