The Concept of Time and Work

Quantitative aptitude tests the ability of an individual to handle numbers and solve numerical problems using critical analysis of different concepts in mathematics such as average, percentage, time and work, etc. Time and work is one such topic from which questions are frequently asked in almost every competitive exam. Hence the concept of this topic has to be very clear, and only then the problem statements on this topic can be attempted correctly. The unique time and work formula is the key to solving and easing particular problems.

What are Time and Work?

Going by basic mathematical definitions, time can be defined as the duration during which a certain activity takes place, whereas work is defined as the set of tasks completed to achieve a desired activity or result. It goes without saying that to complete a work, an amount of time is consumed. It means that there exists a certain relation between time and work.

The mathematical relation between Time and Work

Work done can be defined as the product between the number of persons involved in the work and the number of days taken for the work to be complete. The basic time and work formula is – W = N X D,

Where, W = total work done

  N = number of persons

  D = number of days/time required.

The concept behind Time and Work

The questions on time and work can be of two different types. A problem can include individuals working separately or in combined groups with different individual efficiencies, or there can be problems with combined group efficiency involved.

Now, if a person ‘A’ completes a particular work in X number of days, then work completed by ‘A’ in one day will be = 1/X.

Similarly, if a person ‘B’ completes a particular work in Y number of days, then his work completed in one day will be = 1/Y.

So, if A and B work together, then their combined work done in one day will be (1/X + 1/Y), and therefore A and B together will be able to complete the work in (XY/(X+Y)) days.

Some common examples 

• Ram can complete work in 15 days and Sam in 20 days. They work together for 4 days. Find out the amount of work left.

Answer: 

Work done by Ram in one day = 1/15.

Work done by Sam in one day = 1/20. 

(Ram + Sam) combined one day work = ((1/15)+(1/20)) = 7/60.

(Ram + Sam) combined 4 day work = (7/60)*4 = 7/15.

Therefore, work left = (1-(7/15)) = 8/15.

• A can complete work in 24 days while B can in 40 days. If A and B work together, find out the time taken to complete the work.

Answer:

Work done by A in one day = 1/24

Work done by B in one day = 1/40.

Work done by A and B together in one day = ((1/24)+(1/40)) = 8/120

Therefore, the time is taken by A and B to complete the work = 120/8 = 15 days.

• Raja can do work in 3 days while Karan takes only 2 days. If both of them complete the work together and earn Rs 150. How much does Raja earn?

Answer:

Raja’s wages: Karan’s wages = Raja’s one day work: Karan’s one day work = (1/3) : (1/2) = 2:3

Therefore Raja’s earning = (2/(2+3))*150 = Rs 60.

Tips and Tricks

In example 3, the problem was solved using a simple trick. In competitive exams, the time provided for each question is relatively less, and hence it is very necessary to know the time and work tricks.

Tip 1: Ratios of wages of individuals doing work are directly proportional to the ratio of the efficiency of the same individuals.

Tip 2: If X is three times better than Y, then in any given amount of time, X will complete 3 times more work than Y, and hence the ratio of work done,

X:Y = 3:1. Also, it means that Y will take thrice the amount of time required to complete a certain work than X. Therefore, the ratio of time taken,

X:Y = 1:3.

Tip 3: Efficiency is always directly proportional to work done and inversely proportional to time consumed.

Conclusion

The concept of time and work enables us to complete, fulfill and accomplish a task. It is the base and beginning of everyday life. The basic concept of time helps us to plan our work and vice-versa. The relationship between acting every day and completing the work in a time holds an important part of mathematics as well as daily lives. The time and work tricks help to have a deeper understanding of these problems.