**Quantitative Aptitude Time and Work Study Material**

The number of persons (P), the quantity of work (W) and the period of time taken (T) are important variables in problems related to Time and Work. In other words, the amount of work done depends on these factors. There can be several ways of solving such problems but it is always advisable to use the one which is least error-prone and least time-consuming. Further, emphasis must be on understanding the logic/concept underlying the solutions to the problems rather on than memorizing them.

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Time (T) taken to do a work depends not only on how many persons are engaged to do it but also on how efficient they are. Efficiency here means rate of doing the work. This aspect comes into picture when the problem involves comparison of works being done by different categories of persons. For instance, efficiencies of man, woman, boy, girl, in general, are different. Even Efficiency of one man may not be the same as that of the other; but unless otherwise specifically stated in the problem, all men working in a group are assumed to do work with equal efficiency. The same is applicable to any group of women or any group of boys etc.

**Time period** (T) taken to do work is usually given in number of days. But in many Cases, in addition to the number of days, the problem also specifies the number of hours per day that the person is wording. In such cases, we use time (T) in broader sense. That is to say, it includes not ‘ only the number of days for which the person works but also the number of hours per day that he or she works. Thus, time (T) here is the product of number of days (say D) and working hours per day (say H) i.e.;

T=DxH

The problems on Time and Work can be solved by following two methods:

(i) Ratio and Proportion Method : We discussed the application of Ratio and Proportion in the said chapter earlier for solving such problems. ‘

(ii)Unitary Method : This is a very simple and useful method. The only disadvantage of this method is that sometimes it takes too much time to find the answer. But it is easier to understand. The term Unitary is more or less self-explanatory. Unitary means one. In this method we first proceed to reduce the problem to either work done by one person or work done in one day or persons/time required to do one work and so on as per the requirement of the problem. Then, we move to the next stage, step-by-step to arrive at the final result.

**The problems on Time and Work can be solved by following two methods**

(i) Ratio and Proportion Method : We discussed the application of Ratio and Proportion in the said chapter earlier for solving such problems.

(ii) Unitary Method : This is a very simple and useful method. The only disadvantage of this method is that some¬times it takes too much time to find the answer. But it is easier to understand. The term Unitary is more or less self- explanatory. Unitary means one. In this method we first proceed to reduce the problem to either work done by one person or work done in one day or persons/time required to do one work and so on as per the requirement of the problem. Then, we move to the next stage, step-by-step to arrive at the final result.

For example, 10 persons can do a job in 20 days.

(i) How many persons are required to do the same job in 40 days?

(ii) In how many days 20 persons can complete the same job ?

Sol. (i) To do the job in 20 days, we require 10 persons. .’. To do the job in 1 day, we require more number of persons = 10 x 20 persons.

.-. To do the job in 40 days, we require less number of 10×20 ,

persons =10×20/40=5 persons.

(ii) 10 persons do the job in 20 days.

.’. 1 person will do the job in more than 20 days = 20x 10 days

.’. 20 persons will do the job in less number of days

= 20×10/20 =10 days

Here we will solve more simple as well as difficiHtprob¬lems using these methods and also by some other methods. But before that here are some general rules and important guidelines which will help in solving the problems easily and save considerable amount of time.

**Important Guidelines:**

I. If a person can do a work in D days, then work done by him in 1 day is 1/D Conversely, if he can do 1/Dth

of work in 1 day, he will complete the work in D days.

II. If A is n times more efficient than B i.e., A has n times capacity to do work than that of B, A will take of the time taken by B to do the same amount of work.

III. If the number of persons engaged to do a certain work be changed in the ratio Pj : P2, the time required to do the same work will get changed in the inverse ratio i.e.; P2:P1.

For example, if the number of men engaged to do a certain work be increased in the ratio 4 ; 3, the time required to do the same work will decrease in the ratio 3 : 4.

That is to say, the amount of work remaining unchanged, the number of persons and time required to do the work are inversely proportional to each other.

Now we will find the relationship between the three vari¬ables i.e., the amount of work (W) the number of persons

doing the work (P) and the time taken to do the work (T).

From our common sense we can deduce the following conclusions :

(i) More work requires more persons if time to finish the work remains unchanged and vice-versa. In other words, for constant T, P and W have directly proportional relationship.

(ii) If the amount of work (W) to be done is kept unchanged, more persons will take less time to finish it and vice-versa. That is to say, P and T have inversely proportional relationship when W is kept constant.

(iii) More Work requires more time and vice-versa, if the number of persons engaged to do the work remains same. In other words, for constant P, W and Phave directly proportional relationship.

We can combine the above three relations between P, T and W and write, PT/W = Constant

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