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.