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.

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?

It will take Akash 15 days to complete the entire work if he is assisted by Sunil and Rakesh every third day.

Total work done by Akash, Sunil, and Rakesh in 1 day:

Total work = (1/20) + (1/30) + (1/60) = 1/10

Work done by Akash alone in 2 days: Work done = (1/20) × 2 = 1/10

Work done in 3 days (1 day with all three together + 2 days of Akash's work): Work done = (1/10) + (1/10) = 1/5

So, work done in 3 days is 1/5.

Time taken to complete the work: Time = 5 × 3 = 15 days

So, the time taken will be 15 days.

Time and Work in Mathematics

Time and work problems in mathematics deal with determining the amount of work done by individuals or machines working together or separately within a given timeframe. These problems often involve finding the rate of work, the time required to complete a task, or the number of people or machines needed to finish a job within a specified period.

Here are some common concepts and techniques used in time and work problems:

1. Basic Formula: The basic formula used in time and work problems is: Work = Rate × Time

2. Work Rate: The work rate represents the amount of work done per unit of time by an individual or a machine. It's usually expressed as "work per unit time," such as "jobs per hour" or "tasks per day."

3. Time: Time represents the duration or the amount of time required to complete a certain task.

4. Efficiency: Efficiency is the ratio of work done to the time taken. It's often expressed as a percentage.

5. Inverse Variation: In some cases, when more people or machines are added to a task, the time required to complete the task decreases inversely.

6. Work Done Together: When two or more people or machines work together on a task, their individual work rates are added up to find the total work rate.

7. Work Done Separately: When people or machines work on separate parts of a task, their individual work rates are calculated, and the total work done is the sum of their individual works.

8. Fractional Work: Sometimes, a portion of work is done, and the remaining part of the work is to be completed. In such cases, fractional work is considered.

9. Word Problems: Time and work problems often present real-life scenarios where individuals or machines are performing tasks. These problems require translating the given information into mathematical equations and solving for the unknown variables.

10. Iterative Methods: Some complex time and work problems may require iterative methods or trial and error to find the solution.

To solve time and work problems effectively, it's essential to understand the relationships between work, time, and the number of individuals or machines involved. Practice with various types of problems can help build proficiency in solving them.