QA – Basics of Time and Work

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

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