# Education Archive

## Time and work problems the basics Recruitment and Entrance exams will always check the intelligence levels of the candidates. Why because, such subjects will enable them to apply in routine official works to tackle any kind of problems.

Generally Quantitative aptitude subject contains general mathematics in which “Time and work problems” is an inevitable topic. All of the entrance and recruitment exams set the question paper with a few questions from Time and work problems.

It is quite important to solve aptitude problems quickly to score good marks in the exams. Such kinds of time and work problems are really annoying if you not know to solve it. However, once you know the method and formulae to solve the problems, then it is sure you can complete the question with the answer within the stipulated time.

Basic Concepts of Time and Work

If you come to know the basic connection between time and work, man-hours, then the time and work problems can be solved easily. Correlation between problems on time and work to time, distance and speed:

• Speed is equivalent to the rate at which the work is performed
• Distance traveled is equal to the work performed
• Time to travel distance is equal to the time to do work

Work is the effort put to produce for accomplishing a task. A specific amount of time (T) taken to complete a certain work (W).

The rate of work (R) is the number of units of work done per unit time

Hence, Work (W)= Rate (R) Time (T) whenever some work is done. So, we can assume the total work done as one unit in the problems to simplify the computations. In such cases, T = 1 / R (or) R = 1 / T whereas R and T are inversely proportional as RT=W which is a fixed quantity.

The Chocolate Method

To make your calculations intuitive, the work can be considered as chocolates to be consumed instead of total units of work to be done.

Say for example:

If “X” can do a piece of work in 10 days and “Y” can do the same work in 20 days, in how many days can they complete it if work together?

Assume the total amount of work to be done is 10 units (LCM of 10 and 20), then work done by X in one day is 1 units and work done by y is 2 units. Work done by both X and Y in one day is 3 units. So, the time taken by them to complete 10 units of work is 3.3 days.

Work equivalence

Questions based on Man days’ concept, the basic assumption shall be done that all men work with equal efficiency unless stated in the question. The correlation between the number of people working (N), the number of days worked (D), the number of hours worked per day (H) and work quantity (W) for 2 different cases are given below:

NX DX H1  = N2  X  DX H2

W1                                    W2

So, the time and work problems can be done easily by applying various methods and formulae… We shall meet in the next chapter…