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# Introduction to Time and Work

The concepts of ratio and proportion and simple equations are used to solve problems on Time and Work. Hence, it is important to have a clear understanding of the above concepts in order to solve problems in Time and Work.

Work is the effort applied to produce a deliverable or accomplish a task. It can either be done by humans or machines. A certain amount of time (T) is taken to complete a certain work (W). Hence, time and work are related. The number of units of work done per unit time is called the rate of work (R).

Hence, W = R × T.

Whenever some work is done, the total work itself can be taken as one unit. Hence, we generally assume the total work done as one unit in the problems we encounter in order to simplify the computations. In these cases, R = 1/T or T = 1/R. In other words, R and T are inversely proportional as R ×T = W, which is a fixed quantity and they are reciprocals of each other if W = 1.

### Assumptions

• If a person does some amount of work in a certain number of days, then it is assumed that he does the same amount of work every day uniformly, unless otherwise explicitly stated in the

For example, if a person takes 10 days to complete a certain work, he completes one-tenth of the work every day and vice versa. Similarly, if a pipe can fill a cistern in 20 minutes, then the pipe fills one-twentieth of the cistern every minute.

• If more than one person is carrying out a certain work, then it is assumed that the work is shared equally among them unless otherwise it is explicitly stated in the i.e., they complete the same amount of work every day.

For example, if two people take ten days to complete a work, then one person takes twenty days and hence each of them does one-twentieth of the work every day.

• If more than one person is used to carry out the work such that they share the work equally, the rate of doing work increases directly as that of the number of Hence, if M is the number of men used, then W = M × R × T. Thus it can be seen that the number of men is inversely proportional to the number of days. Thus the product M×T remains a constant for a particular work. This product is often called the MAN-DAYS. Therefore, the number of MAN-DAYS required for a particular work is always a constant and this concept is very helpful in solving problems. Hence, for the same work, M1T1= M2T2. This concept is applicable only if the work is shared equally among all the men.
• If two persons A and B individually can complete a work in ‘a’ days and ‘b’ days respectively, then they can complete 1/ath and 1/bth of the work in one day respectively. Therefore, they can do (1/a + 1/b)th of the work together in one day. The number of days required to complete the work can thus be calculated. Alternately, the number of days required to complete a certain work, when two persons A and B who can complete the work individually in ‘a’ and ‘b’ days respectively work together to complete it, is ab/(a+b). These kinds of problems can be calculated easily by assuming the number of units of work as the

L.C.M of a and b instead of unity thus avoiding calculations involving fractions.

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