Time and Work features regularly in MBA entrances, Bank PO entrances, SSC CGL and many more exams.

The formula to calculate Time and work is as follows:

Total work done = Work done in one day * No. of days of work

The amount of work that a person does in one day is the efficiency of that person.

Thus, Total work done = Efficiency * No. of days of work

Hence, No. of days of work = Total work / Efficiency

(since Total work done = Efficiency * No. of days of work )

Hence, as efficiency increases, the number of days needed to finish some work decreases.

(since No. of days of work = Total work / Efficiency)

Example: Suppose, Ankita can build a wall in 6 days while her friend, Brinda, can build the same wall in 3 days. In how many days can Ankita and Brinda build the same wall if they work together?

In this question, we know that Ankita takes 6 days to complete the work.

This means that, in one day, Ankita does 1/6th of the work.

Similarly, Brinda takes 3 days to complete the work.

This means that, in one day, Brinda does 1/3rd of the work.

From this, we can figure out that, working together, these two will do:

1/6 + 1/3 = ½ of the work in one day

(Since 1/6 + 1/3 = 1/6 + 2/6 = (1+2)/6 = 3/6 = 1/2)

Total amount of work done = Work done per day * Number of days

Thus, Number of days needed = Total amount of work / Work done per day

= 1 / (1/2)

Thus, they will need 2 days to complete the work.

Type 2: Pipes and Cistern

Example 2:

A certain bathtub is connected to three taps, A, B and C. Two of the taps fill the bathtub while the third tap empties the bathtub. Tap A alone can fill the bathtub in 2 hours while tap B alone can fill the bathtub in 3 hours. Further, tap C can empty the bathtub in 6 hours. Initially, the bathtub is empty. Now, if all three taps are opened, how long would it take for the tub to be filled?

We know that tap A alone can fill the bathtub in 2 hours.

Thus, in one hour, tap A can fill ½ of the tub.

Similarly, tap B alone can fill the bathtub in 3 hours.

Thus, in one hour, tap B can fill 1/3 of the tub.

Similarly, tap C can drain the bathtub in 6 hours.

Thus, in one hour, tap C can empty 1/6 of the tub.

So, the 3 taps together can fill = 4/6 = 2/3 of the tub in one hour.

(Since ½ + 1/3 – 1/6 = 3/6 + 2/6 – 1/6 = 4/6).

Hence, in order to fill the tub completely, the three taps would take

= 3/2 = 1.5 hours