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### Problem Summary:
1. Akash, Sunil, and Rakesh have individual work completion times of 20, 30, and 60 days, respectively.
2. Akash will work every day, while Sunil and Rakesh will join every third day.
3. The task is to find out how many days it will take for Akash to complete the work with this arrangement.

### Step-by-Step Solution:

1. **Calculate Individual Work Rates:**
   - Akash’s rate: \( \frac{1}{20} \) of the work per day.
   - Sunil’s rate: \( \frac{1}{30} \) of the work per day.
   - Rakesh’s rate: \( \frac{1}{60} \) of the work per day.

2. **Combined Rate for Every Third Day:**
   - On every third day, all three workers work together.
   - Their combined rate on these days:
     \[
     \frac{1}{20} + \frac{1}{30} + \frac{1}{60} = \frac{3 + 2 + 1}{60} = \frac{6}{60} = \frac{1}{10} \text{ of the work per third day.}
     \]

3. **Work Rate for Days without Assistance:**
   - On the remaining two days, only Akash works. His rate is \( \frac{1}{20} \) of the work per day.
   - In two days, he will complete:
     \[
     2 \times \frac{1}{20} = \frac{1}{10} \text{ of the work.}
     \]

4. **Total Work Completed in Each 3-Day Cycle:**
   - Every 3 days, the total work done is:
     \[
     \frac{1}{10} + \frac{1}{10} = \frac{2}{10} = \frac{1}{5} \text{ of the work.}
     \]

5. **Determine Total Days Needed:**
   - Since each 3-day cycle completes \( \frac{1}{5} \) of the work, the entire work (1) will take:
     \[
     5 \times 3 = 15 \text{ days.}
     \]

### Answer:
It will take **15 days** for Akash to complete the entire work with assistance from Sunil and Rakesh every third day.

Would you like more details, or have any other questions?

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### Related Questions:
1. How would the completion time change if Sunil assisted every second day instead of every third day?
2. What would happen if Akash, Sunil, and Rakesh each had a different assigned frequency of assistance?
3. If the team’s work rates changed, how would you recalculate the completion time?
4. What if Sunil and Rakesh could only assist once a week? How many days would be required then?
5. How does adjusting individual work rates impact the total completion time?

### Tip:
When dealing with work rate problems, calculate individual and combined rates carefully. The concept of work per day helps break down complex schedules into manageable steps.

A builder appoints three construction workers Akash, Sunil, and Rakesh on 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?

Learn how to calculate the time it takes Akash to complete a piece of work with assistance from Sunil and Rakesh every third day. This problem involves calculating individual and combined work rates and is suitable for Grades 9-10.

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