Solve Time and Work-Related Problems

The work and time problems require a general idea about the amount of work that is being done in a certain frame of time. To be able to solve that problem, you will be given an adequate amount of information. But, you should be able to analyse the problems completely and reach a conclusion as soon as possible.  It becomes much easier for you to intercept these problems if you can relate to these problems when they are a part of daily life. 

Easy methods to solve Time and work problems in CAT Exam

The problems that are asked regarding work and time mainly consist of problems that are related to the amount of work done or the filling of a tank. In both cases, a certain relation stays the same.

The efficiency for both the cases will be given as:

For the amount of work done;

Efficiency ∝ 1 / Time taken to do the work

For filling a tank;

Efficiency ∝ 1 / Time taken to fill the tank

The relation will stand true even if the question is regarding the flow of water through a river, tunnel or pipe. This is because, in each of the cases, the rate of flow of water will be accounted for. And, that is a property of the work and time relationship. 

The best way to initiate a problem that is based on the work and time will be to break down the statement in the form of fractions and percentages. This can be done by calculating the fraction or percentage of the work that has been completed, or the efficiency with which the work is being carried out. By taking terms in the order of fractions, it will be easier for a person to get to the conclusion without making many mathematical errors. 

Example 1:

Person A can complete a particular job in 12 days, Person B can complete the same job in 15 days. If they work together how many days would it take to complete the job?

Solution:

Amount of work Person A can do in 1 day = (1/12)_{of the total work}

Amount of work Person B can do in 1 day = (1/15)_{of the total work}

If they work together for 1 day then, work completed would be = (1/12 + 1/15)= (3/20)_{of the total work}.

So the total number of days required if they work together would be, 1/(3/20) = 20/3 = 6 days and 16 hours. 

Example 2:

Arijit is 3 times more efficient at completing work than Devdas. If they work together they complete a project in 5 days. If ajit had worked alone on the project how much would it take Ajit to complete it?

Solution 

Let the efficiency of Arijit be “A” ,

And, that of Devdas be “D”. 

Given that, 3D = A 

Now, 5(A+D) = nA  

[5= number of days Arijit + Devdas would take to complete the work together]

[n= number of days Arijit would take to complete the work Alone]

Now, D=A/3, given. 

So, 

5{A +(A/3)}= nA

Or, n=20/3 days. 

So, it would take Arijit 20/3 days to complete the work alone.   

Are time and work important for CAT?

The problems regarding the concept of the work and time carry a considerable weightage in the CAT examination. These problems are included in the quantitative analysis section of the CAT exams. Seeing as this concept has only a certain few types of probes, it is easy to have a grasp of this concept and the topics that are a derivative of their one. 

The problems that are mainly asked regarding this concept include the problems that are about the working capacity or efficiency of a person, or the amount of work that is being done. Also, the concept of the rate of change of a certain quantity is included in this. It is because this concept poses to make up the very basis of the topic which is the rate of change of certain entities.

The CAT examination also covers topics that are based on the movement of water. This can be associated with the rate of flow of water. This rate of flow can be related to a pipe, tunnel, canal or river. In all the cases, the meaning behind this will remain the same. These problems are related to the time measure in which a body will be filled up with the water given the rate of flow of water. 

What are the topics covered under time and work for the CAT exam?

Each year 2 or 3 problems are asked in the quantitative aptitude section of the CAT examination related to this concept. These problems can be of different types but follow the same method to be solved.

The main types of problems that are faced in the CAT relate to the topic of work and time:

• Calculation of the amount of work that is being done in a certain amount of time.

• The rate of change of a certain quantity.

• The efficiency of a person to complete a task.

• The problems related to pipes, canals, or rivers.

• Time taken to fill a tank.

• Calculation of rate of flow of water through a pipe.

Conclusion

The work and time concept of the CAT examination poses only a certain few types of problems. And, these problems only require a small set of formulas to reach a perfect conclusion. As long as you can analyse the word problem that is given to you perfectly, you will be able to solve the problem in a short period. The main problems that are related to this concept consist of the rate change of an entity. If you can get a good grasp of this topic, you will be able to solve all these problems very easily.