  # Time and Work Questions for CAT: Important Formulas, Concepts, Expert’s Tips | Download Sample Questions PDF

By BYJU'S Exam Prep

Updated on: September 13th, 2023 Time and Work Questions for CAT are an important part of Arithmetic section of quantitative ability section. It is an essential topic, and the aspirants can expect 2-3 questions from this chapter. CAT Time and Work Questions are tricky and one needs to prepare well to ace these questions. The concepts for Time and Work remain the same; however, the types of questions may vary.

As per the analysis of previous years’ CAT exams Time and Work Questions for CAT hold weightage, as it includes various other mathematical applications like pipe and cisterns. The difficulty level may vary from year to year, so it is recommended to practise these questions with a proper and constructed approach. Here, our experts have made a detailed analysis of Time and Work concepts that are used in the questions that appear in CAT exams to help the aspirants to prepare for the topic well.

## What are Time and Work Questions for CAT?

The aspirants must be well aware of the concepts and the types of Time and Work CAT Questions that they may face during CAT Exam day. Time and Work Questions for CAT deal with questions like; time taken by an individual or a group of individuals to complete a piece of work and the efficiency of the work done by each of them. So, the basic types of CAT Time and Questions that may be asked in the exam are as follows:

• Find the efficiency of the individual or the group.
• Find the time taken to complete the work by the individual or the group.
• Find the amount of work completed within a certain period by the individual or the group.

## Concepts Related to Time and Work Questions for CAT

Before starting CAT Preparation for time and work questions, the candidates must be aware of the concept related to negative, efficiency and work equivalence. These two are very important, and you must be well versed in these to solve Time and Work Questions for CAT accurately.

### CAT Time and Work Questions – Negative Work

As per the concepts used in Time and Work Questions for CAT, negative work increases work time. For example, there are two people, X and Y, who are working on making a table. Assume that there is another person, Z, who is assigned the task of damaging the table. In this case, the work done by Z is known as negative work, as Z lowers the work done by X and Y.

Consider one more example of Pipe and Cisterns. Suppose there are two pipes, C and D. C is used to fill the cistern, and D empties the cistern. It means that D is working against C. If a leak is developed in this cistern, then it will form a component of negative work; thus, it slows down the work done by C.

☛ Check CAT Syllabus and make section-wise preparation for all three sections of the exam.

### Time and Work Questions for CAT – Work Equivalence

As per the concepts of Time and Work CAT Questions, the work done by people/cistern can be stated mathematically as follows:

Work done = Rate of Work x Time

Note the formula that is given below as well:

M1D1T1 = M2D2T2

Here: D= Days, M=Person Number, T=Hours

This equation is known as the formula of work equivalence for Time and Work Questions for CAT.

### Time and Work CAT Questions – Efficiency

As per the concept of Time and Work Questions for CAT, the two variables are said to be inversely proportional if their product is always constant. If A is twice as good as B then A will take half the time that B will take because efficiency and time required are inversely proportional.

If the efficiencies are in a ratio format, like M: N, then time will also be in a ratio format, N: M.

## Time and Work Questions for CAT PDF

The candidates who are thinking of appearing in the upcoming exam must practice CAT Time and Work Questions to grip on these questions. Click on the link below to download Time and Work Questions for CAT.

## Sample Questions of Time and Work Questions for CAT

Question 1: A water tank has three taps: A, B, and C. A fills 4 buckets in 24 min, B fills 8 buckets in 1 hr, and C fills 2 buckets in 20 min. If all the taps are opened together, then a full tank is emptied in 2 hr. If a bucket contains 5 L of water, then what is the capacity of the tank?

(a) 120 L

(b) 240 L

(c) 180 L

(d) 60 L

Solution: The capacity of the bucket, as mentioned in the question, is 5 litres

So, tap A fills 20 litres of water in 24 min.

Tap B fills 40 litres of water in 60 min

Tap C fills 10 litres of water in 20 min

So, the work done by all the taps together in 2 hours

= {(20/24*120)+(40/60*120)+(10/20*120)}

= 240

Answer: Thus, the capacity of the tank is 240 litres.

Question 2: A builder appoints three construction workers, Akash, Sunil, and Rakesh, to one of his sites. They take 20, 30, and 60 days respectively, to do a piece of work. How many days will it take Akash to complete the entire work if he is assisted by Sunil and Rakesh every third day?

1. 10 days
2. 15 days
3. 25 days
4. 30 days

Solution: Total work done by Akash, Sunil and Rakesh in 1 day = {(1/20) + (1/30) + (1/60)} = 1/10 Work done by Akash in 2 days = (1/20) × 2 = 1/10

Work Done in 3 days (1 day of all three together + 2 days of Akash’s work) = (1/10) + (1/10) = 1/5

So, work done in 3 days = 1/5

Time is taken to complete the work = 5×3 = 15

## Types of Time and Work Questions for CAT

If you check the CAT Previous Year Question Paper, you will know that there are some specific types of Time and Work CAT questions. The two most important types of Time and Work CAT Questions are as follows:

• Problem involving Group Efficiencies: In this type of question, the aspirant needs to look at the problem where the people having the same efficiencies are working in a group.
• Problem involving Individual Efficiencies: In this type of Time and Work Questions for CAT, you have to look at the individual efficiencies that are required to perform work. The calculation is required to find the rate at which they can complete the whole work together.

☛ Make a list of CAT Books. Solve multiple Time and Work Questions for CAT regularly to understand the concept and improve the efficiency of solving them in the exam.

## Important Formulas for Time and Work CAT Questions

It is very important to know the shortcut formula tricks to solve Time and Work Questions for CAT accurately. Note the below points for important formulas for CAT Time and Work questions.

• Rate of Work = 1 / Time Taken
• Work Done = Time Taken × Rate of Work.
• Time Taken = 1 / Rate of Work
• Efficiency and Time are inversely proportional to each other.
• If a piece of work is done in X number of days, then the work done in one day = 1/X
• Total Work Done = Number of Days × Efficiency
• X: Y is the ratio of the number of men who are required to complete a piece of work, then the ratio of the time taken by them to complete the work will be Y: X
• If x number of people can do W1 work, in D1 days, by working T1 hours each day and the number of people can do W2 work, in D2 days, by working T2 hours each day, then the relation between them will be = (M1*D1*T1)/W1 = (M2-D2*T2)/W2

## Tips to Solve Time and Work Questions for CAT

While solving CAT Time and Work Question, the aspirants must keep in mind the tricks that are given below.

• Tip 1: Wages and Work Concept: The ratio of the wages of the people doing work is directly proportional to the efficiency ratio of the people.
• Tip 2: The ratio is directly and inversely proportional to the work done and time, respectively, as per the mathematical concept.
• Tip 3: The time is taken or the number of days that are required to complete the work by C and D are both equal to the cd/c+d.
• Tip 4: If X can complete the total work in 15 days, then X will perform 1/15 part of the total work in 1 day.
• Tip 5: If C is thrice as good as D, then we can write the following:
• In a certain period of time, C will perform 3 times more work than B. The ratio of the work will be 3:1
• For the same amount of work, D will take the time thrice as much as A takes. The ratio of time taken will be 1:3

Along with the above-mentioned tips to solve Time and Work Questions for CAT, candidates can also solve puzzles for CAT to improve their analytical and reasoning skills.

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