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Shortcuts to solve Time and Work Problems

26-MAR-2018 17:33

    Problems on ‘Time and Work’ are very common in competitive exams like Banking, SSC, CSAT, etc. Knowing the shortcut methods for solving such Quantitative Aptitude problems will give you an edge as most competitive exams also test your time management skills.

    Time and Work  

    Time and Work Basic Formula

    If a person completes a job in ‘n’ days then his 1 day’s work is given by:

    Time and Work

    And his efficiency is given by:

    Time and Work

    Relationship between Efficiency and Time

    Time and Work

    Efficiency and Time are inversely proportional , i.e., if X is 50% efficient as Y, then X takes twice the time taken by Y or if X is twice efficient as Y then X takes half the time taken by Y to finish the job.

    Learn the formulas and shortcuts of Ratio and Proportion

    Time and Efficiency in Ratio

    If the ratio of efficiency of A and B is x: y, then the ratio of the time taken to finish the job by them is:

    Time and Work

    Relationship between Time, Constant Work and Efficiency

    Time and Work

    When the work done is considered in terms of fraction, then the whole work is represented as 1. When the work done is considered in terms of percentage, then the whole work is represented as 100%.

    As mentioned before,

    Time and Work

    As 1 is a constant and considered fraction,

    Time and Work

    Therefore,

    Time and Work

    And when considered in percentage,

    Time and Work

    Learn the basic concepts and formulas of Percentage

    Some Shortcut formulas:

    Time and Work

    •    If A does a work in ‘a’ hours and B in ‘b’ hours then they can together do the job in:

     Time and Work

    •    If A takes ‘a’ hours more than the time taken by A and B together to do a job and if B takes ‘b’ hours more than the time taken by A and B together to do the same job, then they can together finish the job in:

    Time and Work

    •    If A does a job in ‘a’ hours and A and B together take ‘x’ hours to finish a job then B alone will take:

    Time and Work 

    •    If A does a job in ‘a’ hours and B in ‘b’ hours and  A, B and C together in ‘x’ hours to finish a job then:

    I.    C alone will take

    Time and Work

    II.    A and C together will take

    Time and Work

    III.    B and C together will take

    Time and Work

    Example: Priya can do a piece of work in 16 days while Riya can do the same work in 20 days. How long should it take both Priya and Riya to do the same work together?

    Time and Work Example

    Solution:  

    Time and Work

        Both Priya and Riya together can finish the work in

    Time and Work

    If you found this video on ‘Shortcuts to Solve Time and Work Problems’ useful, then do visit www.jagranjosh.com for more such videos on Quantitative Aptitude.

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