Problem: A builder appoints three construction workers Akash, Sunil, and Rakesh to one of his sites. They take 20, 30, and 60 days respectively to do a piece of work. How many days will it take Akash to complete the entire work if he is assisted by Sunil and Rakesh every third day?

Solution:

Step 1: Understand the problem and gather the given information.

- Akash takes 20 days to complete the entire work.
- Sunil takes 30 days to complete the entire work.
- Rakesh takes 60 days to complete the entire work.
- Akash will be assisted by Sunil and Rakesh every third day.

Step 2: Calculate their individual work rates.

- Akash's work rate = 1/20 (1 work per 20 days)
- Sunil's work rate = 1/30 (1 work per 30 days)
- Rakesh's work rate = 1/60 (1 work per 60 days)

Step 3: Find the combined work rate of Akash, Sunil, and Rakesh.

- Combined work rate = Akash's work rate + Sunil's work rate + Rakesh's work rate
= 1/20 + 1/30 + 1/60
= 3/60 + 2/60 + 1/60
= 6/60
= 1/10 (1 work per 10 days)

Step 4: Determine the work done by Akash, Sunil, and Rakesh every third day.

- On the first day, Akash works alone and completes 1/20th of the work.
- On the second day, no work is done.
- On the third day, Akash is assisted by Sunil and Rakesh. Together, their combined work rate is 1/10. So, they complete 1/10th of the work in one day.
- The process repeats every three days: Akash works alone on the fourth day, no work on the fifth day, and Akash is assisted by Sunil and Rakesh on the sixth day to complete 1/10th of the work.

Step 5: Calculate the number of cycles required to complete the entire work.

- In each cycle of three days, 1/20 + 1/10 = 3/60 + 6/60 = 9/60 = 3/20 of the work is completed.
- To complete the entire work, we need 20 cycles because 20 * (3/20) = 3/20 * 20 = 3 work is completed.

Step 6: Determine the total number of days required for Akash to complete the entire work.

- In each cycle of three days, 1/10 of the work is completed.
- So, in 20 cycles of three days, 20 * 3 = 60 days are required to complete the entire work.

Conclusion: Akash will take 60 days to complete the entire work if he is assisted by Sunil and Rakesh every third day.