Time and Work involves dealing with the rate at which individuals or group of people work. Conventionally we start by assuming the number of days (T) taken by a single person to complete a certain task where the rate of work of the person, or the amount of work the person can do in one day, is represented as 1/Tth part of the work.

Rate of work is the most important concept in Time and Work problems because it makes it possible, to sum up the effort of different people working together where each of them has a different rate of work over a unit of time.

Important Terms for Time and Work Formulas-

Before we plunge into time and work formulas, let’s quickly go through the different terms that make up time and work formulas-

Work (W) – The total amount effort or labour required to complete a given task is called work. It is represented by the letter ‘W’ and is always considered as a whole or one in every problem.

Person/ People (P) – The number of individuals involved in completing the given work is called people/person. It is represented by the letter ‘P’.

Time (T) – The exact count taken by the clock to complete a certain task is called time. It is represented by the letter ‘T’. Time can be calculated in two ways- the number or days ‘D’ or the number of hours ‘H’.

Rate of Work (R) – The amount of work done in a unit of time is called the rate of work. It can be calculated on a daily or hourly basis, depending on the conditions given in the questions. It is represented by the letter ‘R’.

Important Formulas - Time and Work

  1. If A can do a piece of work in n days, work done by A in 1 day = 1/n
  2. If A does 1/n work in a day, A can finish the work in n days
  3. If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can do W2 work in D2 days working H2 hours per day (where all men work at the same rate), then M1 D1 H1 / W1 = M2 D2 H2 / W2
  4. If A can do a piece of work in p days and B can do the same in q days, A and B together can finish it in pq / (p+q) days
  5. If A is thrice as good as B in work, then

Ratio of work done by A and B = 3 : 1

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