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Time and Work

Important Formulae

1. Work from Days:

If A can do a piece of work in n days, then A's 1 day's work = 1/n

2. Days from Work:

If A's 1 day's work = 1/n, then A can finish the work in n days.

3. Ratio:

If A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3 : 1
Ratio of times taken by A and B to finish a work = 1 : 3

General Tips

The single most useful formula for the topic Time and Work is
N1H1D1E1W2 = N2H2D2E2W
Where:

N1 and N2 = number of person
H1 and H2 = Hours worked by per person per day (assumed constant)
D1 and D2 = days
E1 and E2 = Efficiency
W1 and W2= Amount of work done

Example 1:
A piece of work can be done by 16 men in 8 days working 12 hours a day. How many men are needed to complete another work, which is three times the first one, in 24 days working 8 hours a day. The efficiency of the second group is half that of the first group?
Solution
N1H1D1E1W2 = N2H2D2E2W1
16*12*8*1*3 = N2*8*24*0.5*1
N2 = (16*12*8*1*3)/ (8*24*0.5*1) = 48
So number of men required is 48
Note :
you can remove anything from formula is not given in the question. For example if the question would have been – “A piece of work can be done by 16 men in 8 days working 12 hours a day. How many men are needed to complete another work, which is three times the first one, in 24 days working 8 hours a day.” The applicable formula would have been:
N1H1D1W2 = N2H2D2W1
Here nothing is mentioned about efficiency, we remove it from both sides.
Example 2
A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
Solution

Let A's 1 day's work = x and B's 1 day's work = y.
Then, x + y =1/30 and 16x + 44y = 1.
Solving these two equations, we get: x = 1/60 and y = 1/60
B's 1 day's work = 1/60
Hence, B alone shall finish the whole work in 60 days.