Posted by: catindiaonline | October 25, 2008

CAT Quant : Work based problems fundas

In this lesson we will discuss one of the most easiest and important topic i.e. WORK.

DEFINITION


Technically speaking, Work is the quantity of energy transferred from one system to another but for question based on this topic-

Work is defined as the amount of job assigned or the amount of job actually done. Problem on work are based on the application of concept of ratio of time and speed.

Work is always considered as a whole or one. There exists an analogy between the time-speed-distance problems and work.

Work based problem are more or less related to time speed and distance.

Above mentioned definition of work throws light on three important points.

  • Work = 1 ( as it is always measured as a whole) = Distance
  • Rate at which work is done = speed
  • Number of days required to do the work = Time

IMPORTANT FORMULAE FOR WORK RELATED PROBLEMS


  1. If A can do a piece of work in ‘a’ number of days, then in 1 day \frac{1}{a} thof the work is done. Conversely, if a man does \frac{1}{a} th of work in a day, then he can complete the work in \frac{1}{\frac{1}{a}} = a days.

    Example: If a man can complete a work in 10 days. How much work he can do in 6 days?

    Solution:
    A man performs in 10 days = 1 work.

    => A man will perform in 1 day = \frac{1}{10} work

  2. If A is ‘x’ times as good a workman as B, then he will take \frac{1}{x} th of the time by B to do the same work.

    Example: If A can complete a work in 10 days and B is 100% faster than A. How much time B will take to complete the work?

    Solution:
    A takes to perform 1 work = 10 days.

    => B will perform the same work = \frac{1}{2} time than A.

    => B will take to perform the same work = 10 days * \frac{1}{2} = 5 days

  3. If A and B can do a piece of work in ‘a’ days and ‘b’ days respectively, then working together, they will take \frac{xy}{x + y} days to finish the work and in one day, they will finish \frac{x + y}{xy} th part of work.

For rest go to CAT India Online’s CATclub

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