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Quantitative Aptitude :: Time and Work

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Time and Work Important Formulas

Time and work problems always hold its importance in almost all competitive exams. Most of the IT companies placement papers (TCS, Capgemini, Wipro, CTS, Infosys, IBM, HCL etc.), and other competitive exams (AMCAT, Cocubes, Elitmus, CAT, XAT, MAT, GRE, GMAT etc.) questions papers will have at least 1 or 2 questions from this topic. There are basically 13 types of Time and work problems. If you practice all of them then you can solve almost every type of questions from this section. In our Arithmetic aptitude tutorial series, we will first discuss formulas used across exercise, which will help you to solve basic and standard based on Time & Work. Moving forward on the same track, we will take each type of time and work question and approach to solution by following step-by-step solution, along with that we will follow shortcut method to approach to solution.

Go through the formula followed by solved examples of each type and practice all type of questions based on each type from Time & Work practice section. In case you find a better approach Step-by-Step/Shortcut/Tips you can mention them in the comment box.
So brace yourselves by revising the basic concepts and time and work formulas and get started for efficiency based time and work problems.

Some basic terminologies one should know before beginning:
1) Work done (w) - The total amount of effort required to complete a given task is called work. We will denote work as w.
2) Person (p): Person stands for the number of individuals required to complete the work.
3) Time (t): The exact count taken by the clock to complete a certain task is called time.
4) Rate of Work (r):Work done per unit time is called r.

Relationship b/w above Terms:
Work done is always proportional to the number of people doing the work provided the time is constant.
Hence: w ∝ p (t = constant) It means more people will be able to do more work in a given unit time.
Work done is always proportional to the time taken to do the work provided that the number of People's is constant.
Hence: w ∝ t (p = constant) It means that more work requires more time keeping the number of people constant. Here time can be in hours and days also.

  1. To Find Work from Days:

    If A can do a piece of work in 'n' days, then A's 1 day's work = \(\frac{1}{n}\).
  2. To Find Days from Work:

    If A's 1 day's work = \(\frac{1}{n}\) , then A can Finish the work in n days.
  3. To Get Ratio:

    If A is thrice as good a workman as B, then:

    Ratio of work done by A and B = 3 : 1.

    Ratio of times taken by A and B to finish a work = 1 : 3.