Problem:
A, B, and C can do a piece of work in 20, 30, and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

Solution:
To solve this problem, we need to figure out the work done by A, B, and C individually and then determine the combined work done by A, B, and C on every third day.

Step 1: Individual Work Rates:
Let's calculate the work done by A, B, and C individually in one day.

Work done by A in one day = 1/20
Work done by B in one day = 1/30
Work done by C in one day = 1/60

Step 2: Combined Work on Every Third Day:
Now, let's calculate the combined work done by A, B, and C on every third day.

On the first day, A works alone and completes 1/20th of the work.
On the second day, A works alone again and completes another 1/20th of the work.
On the third day, A is assisted by B and C. So, in one day, A completes 1/20th of the work, B completes 1/30th of the work, and C completes 1/60th of the work. Therefore, combined work done on the third day = (1/20 + 1/30 + 1/60) = 1/12.

This pattern continues, with A working alone on the 4th and 5th days, and A being assisted by B and C on the 6th day. The combined work done on every third day remains constant at 1/12.

Step 3: Total Work Done:
Now, let's calculate the total work done by A, B, and C over a given period.

In 6 days, A completes 2/20 = 1/10th of the work.
In 6 days, B completes 2/30 = 1/15th of the work.
In 6 days, C completes 2/60 = 1/30th of the work.

Since the combined work on every third day is 1/12th, the total work done by A, B, and C in 6 days is 1/12th.

Step 4: Final Calculation:
Now, let's determine how many sets of 6 days are required to complete the entire work.

Let the total number of sets be x.
Therefore, the total work done in x sets of 6 days = x * (1/12) = x/12.

As per the given information, A, B, and C can complete the work individually in 20, 30, and 60 days respectively.
Therefore, the total work done in x sets of 6 days should be equal to the work done by A in 20 days.

x/12 = 1/20
x = 12/20
x = 3/5

Since each set of 6 days corresponds to 3/5 of a day, the total number of days required for A to complete the work with the assistance of B and C on every third day is:

6