Work and Time Problems are very frequently asked in various competitive exams and they also have a lot of relevance in our day to day life. There are three important entities that you need to understand before you learn ‘How to Solve Time and Work Problems’. These three entities are time, work and people. All types of time and work problems necessarily involve these three entities. There can be different levels of time and work problems, but the concept remains the same. Once you understand the basic concept, you will be able to solve any type of work and time problems.
The Basic Concepts of Work and Time Problems
Let us start with a simple case where one man can complete a certain work in 10 days. When you get that statement in your question, you need to first calculate how much work the man does in one day. It is given by 1/ (No of Days to complete the whole work) i.e. 1/10 in this case. Similarly, if you have another man who can complete the same work in 40 days, then his one day work will be equal to 1/40. Similarly, you can have any number of men in your problem. You just need to calculate everybody’s one day work. Now, when they say that these two men are working together, you simply need to add their one day’s work to calculate their combined one day work. In this case, it will be (1/10 +1/40) = 5/40 = 1/8.
Remember that if one day’s work = 1 No. of days complete the whole work
Thus, if you know one day’s work, you can calculate the no of days it will take to complete the whole work.
Total no days required to complete the whole work = 1/one day's work
In the given problem, if two men start to work together, they will take 8 days to complete the whole work as their one day’s work is 1/8.
Suppose we are given that x number of men can complete a work in y days, then
Work done by x men in one day = 1/y
Work done by one man in one day = 1/x * 1/y = 1/ (xy)
For example: If 10 men complete a work in 20 days, then x = 10 and y =20. So,
Work done of one man in one day = 1/ (10*20) = 1/200
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