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
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