Time and Work: Concepts, Formulas & Solved Aptitude MCQs [Examples]

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Understanding the concepts and formulas of time and work is essential for solving aptitude questions efficiently. These questions often appear in exams like UPSC, SSC, Banking, CAT, and campus placements. In this article, we will break down the key concepts and definitions of time and work with examples, provide you with tips and tricks, and solve Multiple Choice Questions (MCQs). 

Concepts and Definitions Related to Time and Work

1. Work: In aptitude problems, "work" usually refers to a job or task that needs to be completed. The total work is often assumed to be 1 unit (for simplicity) unless otherwise specified.

2. Time: Time is the duration required to complete a work.

3. Rate of Work: The rate of work refers to how much part of the job is done per unit of time (usually per day or per hour).

4. Work Done: The work done tells how much of the job is completed in a certain amount of time.

5. Efficiency: Efficiency is the amount of work a person (or machine) can do in one day. More efficiency means less time is required to complete the work.

7. Inverse Relation Between Time and Number of Workers: If more workers are assigned to a task, the time taken decreases, assuming equal efficiency and continuous work.

8. Combined Work: When two or more people work together, their combined rate is the sum of their individual rates.

Important Time And Work Formulas

Let us now study some of the most common key formulas used in time and work-related aptitude questions: 

1. Work Done = Time Taken × Rate of Work

2. Rate of Work = 1 / Time Taken

3. Time Taken = 1 / Rate of Work

4. If a job is completed in ‘n’ days, then work done in 1 day = 1/n

5. Total Work Done = Number of Days × Efficiency

6. Efficiency and Time are inversely proportional:

   • If efficiency increases, time decreases, and vice versa.

   • Mathematically: Efficiency × Time = Constant

7. If M : W is the ratio of the number of men to women required to complete a task, then the ratio of time they take to complete the same work is W : M.

8. General Formula for Two Work Conditions: M₁×D₁×T₁×W₂=M₂×D₂×T₂×W₁​

Where:

• M₁,D₁,T₁ = men, days, hours per day in the first case

• M₂,D₂,T₂ = men, days, hours per day in the second case

• W₁,W₂​ = amount of work in each case

Tricks and Tips to Solve Time & Work Questions

To effectively solve time and work quantitative aptitude questions, follow the tricks and tips provided below:

• Always assume total work = LCM of given days to avoid decimals.
• Efficiency × Time = Total Work → Use to compare workers.
• Carefully track when workers enter or leave a task.
• Understand the question pattern (full work, part work, combined work, alternate days, etc.)

Time And Work MCQs with Detailed Solution 

Provided below are some selected top questions with detailed answers related to time and work:

Question 1. A piece of work assigned to Binu and Vinu can be completed in 28 days. Their friend Manoj came, and they could finish it in 21 days. How long will it take for Manoj to finish the work alone?

(a) 84 days

(b) 80 days 

(c) 75 days

(d) 70 days

Solution: a) 84 days

Explanation:

Binu + Vinu = 1/28 

Binu + Vinu + Manoj = 1/21

Manoj = 1/21 – 1/28 = 1/84

Therefore, Manoj will take 84 days to do the work. 

Question 2. Two friends, Ajay and Vijay together, can do a piece of work in 6 days. Ajay alone does it in 10 days. What time does Vijay require to do it alone?

(a) 20 days

(b) 15 days 

(c) 25 days

(d) 30 days

Solution: b) 15 days

Explanation:

Given that Ajay and Vijay together can complete a work in 6 days. This means that their combined work rate is Ajay + Vijay = 1/6

Ajay alone can complete the same work in 10 days. This implies that Ajay's work rate = 1/10. We need to find out Vijay's work rate by subtracting Ajay's work rate from the combined work rate of Ajay and Vijay: 1/6 – 1/10 = 2/30 = 1/15

Vijay's work rate is 1/15. 

Let’s now find out how many days it would take for Vijay alone to complete the work. Vijay work rate is 1/15 of the work per day. Therefore, time taken by Vijay alone=1/15 =15.

Question 3. Abbot can do some work in 10 days, Bill can do it in 20 days, and Clinton can do it in 40 days. They start working in turns, with Abbot starting to work on the first day, followed by Bill on the second day, Clinton on the third day, and again by Abbot on the fourth day, and so on till the work is completed fully. Find the time taken to complete the work fully.

(a) 16 days

(b) 15 days 

(c) 17 days

(d) 16.5 days

Solution: d) 16.5 days

Explanation:

The work rate would be 10% on the first day, 5% on the second day, and 2.5% on the third day. For every block of 3 days, 17.5% of the work would be done. In 15 days, the work completed would be 17.5 X 5 = 87.5%. On the 16 days, work done = 10% 

2.5% of work would be left after 16 days. On the 17th day, the rate of work would be 5%, and hence, it would take half of the 17th day to complete the work. Thus, it would take 16.5 days to finish the work in this fashion.

Question 4. It takes x hours for a pipe to fill a tank, while another pipe can empty it in y hours. If the tank is 1/3rd full, then the number of hours in which they will together fill it in is

a) (3xy)2(y-x)   

b) (3xy)(y-x)  

c)(xy)3(y-x) 

d) (2xy)3(y-x)

Solution: d) (2xy)3(y-x)

Explanation:

One can fill the tank in x hours, and the other can empty the tank in y hours. The rate of filling of the first pipe is 1/x tank per hour, and the rate of emptying of the second pipe is 1/y tank per hour.

Consider that the tank is already full 1/3, which means the remaining tank needs to be filled 2/3. The net rate of filling the tank is the sum of the rates of filling by the first pipe and emptying by the second pipe. Net rate of filling= (1/x) – (1/y)

We want to find the time it takes for the pipes to fill the remaining of the tank together. The work done by the pipes in T hours working together is equal to 2/3.

(1/x – 1/y).T = 2/3

T= 2/3 x (1/x-1/y)

T = 2/3 (xy)/(y - x) 

T = 2 xy /3(y-x)

The number of hours in which the pipes together will fill the tank is T = 2 xy /3(y-x).

Question 5. A finishes 6/7th of the work in 2 hours, and B works twice as fast and finishes the remaining work. For how long did B work?

(a) 15 minutes

(b) 30 minutes

(c) 45 minutes

(d) 60 minutes

Solution: d) 60 minutes

Explanation:

Since A finishes 6/7th of the work in 2 hours, A completes 6/7 * 1/2 = 3/7th of the work in 1 hour. Now, since B works twice as fast as A, B completes the same amount of work (3/7th) in half the time it takes A.

Therefore, B finishes the remaining 1/7th of the work in 1/2 * 2 = 1 hour. So, the time taken by B to finish the remaining work is 1 hour, which is equivalent to 60 minutes.

Question 6. A can do a piece of work in 20 days, and B can do it in 15 days. If C, who can finish the same work in 25 days, joins them, then how long will it take to complete the work?

a) 6 (18/47)days   

b) 12 days   

c) 2 (8/11) days    

d) 47 (6/18) days

Solution: a) 6(18/47) days

Explanation:

 A’s work = 5% per day 

B’s work = 6.66% per day 

C’s work = 4% per day. 

Total no. of days = 100/15.66 = 300/47 = 6(18/47)

Question 7. Sambhu can do 1/2 of the work in 8 days, while Kalu can do 1/3 of the work in 6 days. How long will it take for both of them to finish the work?

a)(88/17)days   

b) (144/17)days    

c) (72/17)days 

d) 8 days      

Solution: b) (144/17)days

Explanation:

Sambhu requires 16 days to do the work, while Kalu requires 18 days to do the work. 

(1/16 + 1/18) X n = 1

n = 288/34= 144/17

Question 8. Anmol is thrice as good a workman as Vinay and, therefore, can finish the job in 60 days less than Vinay. In how many days will they finish the job working together?

a) 22.5 days  

b)12.5 days  

c) 15 days 

d) 20 days

Solution: a) 22.5 days

Explanation:

Anmol takes 30 days, and Vinay takes 90 days. Consider Vinay takes x days to finish the job, and Anmol, being three times better than Vinay, takes x/3 days to finish the same job. Anmol can finish the job in 60 days less than Vinay.

Anmol's time = Vinay's time - 60

x/3 = x - 60

x = 3(x - 60) = 3x - 180

2x = 180

x = 90

Vinay takes 90 days to finish the job. Now Anmol's time: x/3 = 90/3 = 30

Combined work rate = 1/30+ 1/90

                3/90+1/90 = 4/90

       Number of days = 1/Combined work rate

                    1/(4/90) = 90/4

                                  =22.5

Question 9. Anju, Manju, and Sanju can reap a field in 6 days. If Anju can do it alone in 10 days and Manju can do it in 24 days, in how many days will Sanju alone be able to reap the field? 

(a) 40 days

(b) 36 days

(c) 35 days

(d) 32 days

Solution: a) 40 days

Explanation:

Total work of Anju, Manju and Sanju = 16.66% 

Anju’s work = 10% 

Manju’s work = 4.166% 

Sanju’s work = 2.5% 

So Sanju can reap the field in 40 days.

Question 10. 5 women can paint a building in 30 working hours. After 16 hours of work, 2 women decided to leave. How many hours will it take for the work to be finished?

(a) 16.66 hours

(b) 40.22 hours

(c) 35.66 hours

(d) 39.33 hours

Solution: d) 39.33 hours

Explanation:

Let the work finish in x hours. 

5 x 30 – 5 x 16 = 3 x (x – 16)

By solving, we get 

150 - 80 = 3x - 48

70 = 3x - 48

3x = 70+48

3x 118

X = 118/3 = 39.33 hours.

Conclusion

Exploring time and work concepts, formulas, problem-solving strategies, sample questions, aptitude practice, question pattern analysis, and learning benefits has equipped individuals with a solid foundation in this area. By honing these skills, individuals can boost their confidence when facing similar challenges during placement interviews and exams.

Time For A Short Quiz

Frequently Asked Questions (FAQs)

1. What is the relation between time and work?

Time and work go together because the time you spend on a task affects how much work you can do. More time usually means more work done, but remember that the quality of work can also be affected by the time spent.

2. What is the formula for time and work together?

The formula for time and work together is based on the principle that the rates at which individuals work are additive. Here's the formula:

If A can complete a job in 'a' days and B can complete the same job in 'b' days, then: time taken when working together=Work done by A in one day × work done by B in one day/ Work done by A and B together in one day.

3. What is an example of a time and work problem?

A time and work problem is when you figure out how much time a group of workers needs to finish a task based on how long each worker takes to do it alone. This kind of problem requires creating equations to find out how fast each worker finishes the task. Then, we use this information to figure out the total time it takes for all workers to finish the task together.

4. Where can one find additional practice questions related to time and work?

Additional practice questions related to time and work can be found in aptitude test preparation books, online platforms offering mock tests or quizzes, educational websites specializing in mathematical topics, coaching institutes providing study materials or worksheets, or mobile apps designed for aptitude practice.

5. Why is it important to analyze exam question patterns related to time and work?

Analyzing exam question patterns helps identify common types of questions asked in tests or exams on time and work topics, understand the weightage given to different concepts within the subject area, tailor preparation strategies accordingly to focus on high-yield areas, and familiarize oneself with the format of questions likely to be encountered.

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