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Sunday, 29 October 2017

Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB

Mahendra Guru

Time and Work:

In most of the problems on time and work, one of the following basic parameters is to be calculated:
  1.    TIME:   Time needed by more than one person to complete a job or time for which a person(s) actually worked on the assigned job.
  2.   ALONE TIME: Time needed by single person to complete a job.
  3.   WORK: The amount of total work (assigned) or the part of total work actually done.
  4.   Efficiency :   One day work by a person is called efficiency
  5.   Time :         Time =  Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB
  1.   Time and work (or work efficiency) both are inversely proportional to each other
  2. Time   Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB

                           A         B
 Time                5    :    4
Efficiency         4    :    5
  1.   Wages always distributed in the proportional of work (or work efficiency )
 
  Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB =  Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB                                                                              
                
                  M  =   Number of workers
                  D  =    Number of working days
                  H  =     Working hours in one day
                  W  =     Unit of work ( Wages)

Ex:  24 men can do a piece of work in 12 days if they work 8 hours per day. Find the number of days in which 36 men can do 6 hour per day ?

Sol:  From-               Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB  =  Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB
                       Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB = Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB
                                   D2 = Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB
                                        = 10Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB  days

Ex:  36 men can do a piece of work in 8 days, if they work 6 hours per day. Find the number of days in which 24 men can do half work , if they work 8 hours per day ?
Sol:   From-               Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB = Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB
                               Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB = Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB
                                          D2 = Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB
                                           Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB days

Ex:  24 man can do a piece of work in 16 days they start the work but after 8 days 12 man leave the work. Find the number of days in which total work become complete ?

Sol:
 From,             Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB      = M1D1 + M2 D2
                    24 X 16    = ( 24 X 8 + 12 X D2)
                      12 x D2   = 384 Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB
                                                     = 192
                                             D2  = 16 days

Ex:  Ram can do a piece of work in 20 days and Mohan can do same work in 30 days. Find the number of days in which total work become complete if they work together?

Sol:            
                     RAM            MOHAN
                       20                    30
    Efficiency    3                       2
                ( R + M ) =    (3 +2 )
                                =    5      
Time = Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB
           = Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB  = 12 days                
              
Ex: Rohan can do a piece of work in 36 days but with the help of Mohan he can complete whole work in 24 days find the number of days in which Mohan alone can complete whole work ?

                     Total Work = 72
Sol:            
                           R                ( R + M)                      
                         36                      24
      Efficiency   2                         3
                   M    =    (3 - 2 )
Time = Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB
           = Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB  = 72 days  
 
Ex:  ‘A’ can do a piece of work in 20 days and ‘B’ can do same work in 12 days .Find the number of days in which they can complete the whole work if work on alternate days and work is started by ‘A’ ?

                                              T.W.= 60
A                B
                                          20                12
Efficiency     à                3         +       5
2 days work = 3 + 5 = 8
14 days work = 8 x7 = 56
Till the 15th  day work is (A) = 56 + 3
                                                = 59
On the 16th day     Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB (B) = 1 work
No. of days = 15Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB

Ex: ‘A’ and ‘B’ can do a piece of work in 30 days, while ‘B’ and ‘C’ can do the same work in 24 days and ‘C’ and ‘A’ in 20 days. They all work together for 10 days Then ‘B’ and ‘C’ left. In how many more days will ‘A’ take to finish the work ?

T.W. = 120
                                         A+B              B+C                              C+A
                                         30                   24                                  20
Efficiency                       4      +               5     +                               6
A+B +C = Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB
10 Days work = 7.5 x 10 = 75
Remaining work = 120 - 75 = 45
Time (A) =
             Efficiency(A) = 7.5-5
                   = 2.5
             = 18 days

Ex:  ‘A’ can finish a work in 24 days, ‘B’ in 9 days and ‘C’ in 12 days. ‘B’ and ‘C’ start the work but are forced to leave after 3 days. The remaining work was done by ‘A’ in-
                                        
   Sol:                 Total Work = 72
                           A        B            C                      
                       24          9           12
    Efficiency   3            8            6
     3 Days work(B+C) =    (14X3)
                                   =    42 
      Remaining work  = 7242
                                  = 30
Time(A) = Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB
                 = Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB 
               = 10 days    

Ex: ‘X’ and ‘Y’ can do a piece of work in 25 days and 20 days respectively. Both together work for 5 days and then ‘X’ leaves off. How many days will ‘Y’ take to finish the remaining work. ?
T.W.= 100
X                          Y
25                         20
Efficiency à       4                           5
Efficiency (X + Y)  =  9
5 days work(X + Y) = 5 x 9 = 45
Remaining work = 100- 45
                           = 55
Time(Y) = Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB
=Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB
                  Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB

Ex:  A can build a wall in 30 days, while B alone can build it in 40 days. If they build it together and get a payment of Rs 7000, what is B’s share?
A                B
30        40
Efficiency       4         :        3
Total amount = 7000
B’s share           = Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB x 7000
                         = 3000 Rs

Ex:  ‘A’ is 30 % more efficient than ‘B’, they together can complete a piece of work in 39 days. How many days in ‘A’ alone can complete the work ?
A : B  = 130 : 100
A : B = 13 : 10
Total Efficiency  = (13 +10) = 23
Total work  = (efficiency x Time)
Total work  = 23 x 39                  
Time (A) = Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB
               = 69 days

Ex:  36 men can do a piece of work in 16 days they start the work but after 4 days 6 men replaced by 48 women. Find the number of days in which remaining work become complete if efficiency of 1 woman is 50% than a man ?
Man                  Woman
Efficiency    2         :        1          1 Man  = 2 Women
Total work  = (36 x 2) x 16
= 1152
4 days work = (36 x 2) x 4 = 288
Remaining work = 1152 – 288 = 864
Total men = (36 – 6 + 24) = 54
Remaining days = Important Notes : Problem Based On Time & Work for IBPS PO / IBPS RRB                   Efficiency (54 Men) = 54 x 2
=108
= 8 days




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