Time and Work

In most of the problems on time and work, one of the following basic parameters is to be calculated:

•    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.
•   ALONE TIME: Time needed by single person to complete a job.
•   WORK:The amount of total work (assigned) or the part of total work actually done.
•   Efficiency :One day work by a person is called efficiency
•   Time :         Time =

• Time and work (or work efficiency) both are inversely proportional to each other
• Time

A         B
Time                5    :    4
Efficiency         4    :    5

• Wages always distributed in the proportional of work (or work efficiency )

 = 
                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-                 = 
 =
D2 =
= 10  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-                =
 =
D2 =
 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,                   = M1D1 +M2 D2
24 X 16    = ( 24 X 8 + 12 X D2)
12 x D2   = 384
= 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 =
=   = 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 =
=   = 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 (B) = 1 work
No. of days = 15
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+BB+CC+A
                                         302420
Efficiencyà                     4      +               5     +                               6
A+B +C =
10 Days work = 7.5 x 10 = 75
Remaining work = 120  75 = 45
Time (A) =
Efficiency(A) = 7.55
= 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) =
=
= 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 = 1 45
= 55
Time(Y) =
=

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           =  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) =
= 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 ?
ManWoman
Efficiency    2         :        11 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 = Efficiency (54 Men) = 54 x 2
=108
= 8 days