Work and Time – Amazing Tricks

Basic Concepts of Time and Work

Most of the aptitude questions on time and work can be solved if you know the basic correlation between time, work and man-hours which you have learnt in your high school class.

  • Analogy between problems on time and work to time, distance and speed:
    1. Speed is equivalent to rate at which work is done
    2. Distance travelled is equivalent to work done.
    3. Time to travel distance is equivalent to time to do work.
  • Man – Work – Hour Formula:
    1. More men can do more work.
    2. More work means more time required to do work.
    3. More men can do more work in less time.
    4. M men can do a piece of work in T hours, then Total effort or work =MT man hours 
    5.  Total effort or work =MT man hours.
    6. Rate of work * Time = Work DoneRate of work * Time = Work Done
    7. If A can do a piece of work in D days, then A‘s 1 day’s work = 1/D.
      Part of work done by A for t days = t/D.
    8. If A‘s 1 day’s work = 1/D, then A can finish the work in D days.
    9. MDH/W=Constant
      Where,

      M = Number of men
      D = Number of days
      H = Number of hours per day
      W = Amount of work
    10. If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can do W2work in D2 days working H2 hours per day, then
      M1D1H1/W1=M2D2H2/W2
    11. If A is x times as good a workman as B, then:
      1. Ratio of work done by A and B = x:1
      2. Ratio of times taken by A and B to finish a work = 1:x    i.e.; A will take (1/x)tof the time taken by B to do the same work.

Shortcuts for frequently asked time and work problems

  • A and B can do a piece of work in a days and b days respectively, then working together:
    1. They will complete the work in ab/a+b days
    2. In one day, they will finish (a+b/ab)tpart of work.
  • If A can do a piece of work in a days, B can do in b days and C can do in  c days then,
    A, B and C together can finish the same work in     abc/(ab+bc+ca) days
  • If A can do a work in x days and and B together can do the same work in y days then,
    Number of days required to complete the work if B works alonexy/(xy) days
  • If A and B together can do a piece of work in x days, B and C together can do it in y days and Cand A together can do it in z days, then number of days required to do the same work:
    1. If A, B, and C working together = 2xyz/(xy+yz+zx)
    2. If A working alone = 2xyz/(xy+yzzx)
    3. If B working alone = 2xyz/(xy+yz+zx)
    4. If C working alone = 2xyz/(xyyz+zx)
  • If A and B can together complete a job in x days.
    If A alone does the work and takes a days more than A and B working together.
    If B alone does the work and takes b days more than A and B working together.

    Then,x=√(ab) days
  • If m1 men or b1 boys can complete a work in D days, then m2 men and b2 boys can complete the same work in Dm1b1/(m2b1+m1b2)days.
  • If m men or w women or b boys can do work in D days, then 1 man, 1 woman and 1 boy together can together do the same work in Dmwb/(mw+wb+bm) days
  • If the number of men to do a job is changed in the ratio a:b, then the time required to do the work will be changed in the inverse ratio. ie; b:a
  • If people work for same number of days, ratio in which the total money earned has to be shared is the ratio of work done per day by each one of them.
    ABC can do a piece of work in xyz days respectively. The ratio in which the amount earned should be shared is 1/x:1/y:1/z=yz:zx:xy1x:1y:1z=yz:zx:xy
  • If people work for different number of days, ratio in which the total money earned has to be shared is the ratio of work done by each one of them.

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