Thursday, March 13, 2014

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Time And Work - Aptitude Concepts (Important Facts And Formule)


time-and-work-aptitude-question-answer-concepts-how-to-solve


IMPORTANT FACTS AND FORMULAE


1. If a person say A can do a piece of work in n days, then

A's 1 day's work = (1/n).

2. On the other hand If A’s 1 day's work = (1/n),then

A can finish the work in n days.

3. A is twice as good a workman as B, then:

    The Ratio of work done by A and B = 2 : 1.
    The Ratio of times taken by A and B to finish a work = 1 : 2



SOLVED EXAMPLES


Ex. 1. Worker A takes 8 hours to do a particular job. Worker B takes 10 hours to do the same Job. Then how long should it take both A and B, working together but independently, to do the same job?

Sol.  A’s 1 hour's work = 1/8

        B's 1 hour's work = 1/10

       (A + B)'s 1 hour's work = (1/8) +(1/10)=9/40

       Both A and B will finish the work in 40/9 days.



Ex. 2. A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work? 

Sol. (A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12).
 
       B's 1 day's work =((1/4)-(1/12))=(1/6)

       Hence, B alone can complete the work in 6 days.



Ex 3 .45 men can complete a work in 16 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work?

Sol.  (45 x 16) men can complete the work in 1 day.
 
         1 man's 1 day's work = 1/720
 
        45 men's 6 days' work =(1/16*6)=3/8

        Remaining work =(1-3/8)=5/8
 
        75 men's 1 day's work = 75/720=5/48

Now, 5/48 work is done by them in 1 day.

5/8 work is done by them in (48/5 x 5/8) = 6 days.



Ex. 4. A and B working separately can do a piece of work in 9 and 12 days respectively, If they work for a day alternately, A beginning, in how many days, the work will be completed?

Sol. (A + B)'s 2 days' work =(1/9+1/12)=7/36

       Work done in 5 pairs of days =(5*7/36)=35/36

       Remaining work =(1-35/36)=1/36

       On 11th day, it is A’s turn. 1/9 work is done by him in 1 day.

       1/36 work is done by him in(9*1/36)=1/4 day

       Total time taken = (10 + 1/4) days = 10 1/4days.




Ex. 5. A can do a piece of work in 80 days. He works at it for 10 days B alone finishes the remaining work in 42 days. In how much time will A and B working together, finish the work?

Sol. Work done by A in 10 days =(1/80*10)=1/8

       Remaining work = (1- 1/8) =7/ 8

       Now,7/ 8 work is done by B in 42 days.

      Whole work will be done by B in (42 x 8/7) = 48 days.

       A’s 1 day's work = 1/80 and B's 1 day's work = 1/48

      (A+B)'s 1 day's work = (1/80+1/48)=8/240=1/30

      Hence, both will finish the work in 30 days.

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