Time And Work- Formula & Aptitude Practice Question With Answer

Understanding the concept of time and work is crucial in quantitative aptitude. This topic deals with how efficiently tasks can be completed based on the amount of time and the number of workers involved.

By mastering the formulas and techniques related to time and work, individuals can solve complex problems and optimize productivity.

Time & Work Concepts

Time and work in the context of aptitude tests refer to the time a workman takes to complete a specific task or project. It involves calculating how long it would take for one or more individuals working together to finish a job.

Relationship Between Time, Work & Efficiency

The relationship between time, work, and efficiency is crucial in solving problems related to this concept. Efficiency indicates how much work can be done in a unit of time, influencing the overall completion time of a task.

Time And Work Formulas

Let us study some of the important formulas in time and work:

Work Efficiency

Work efficiency is calculated as total work divided by the total time taken to complete the work. It is denoted by the symbol:

E = Total Work / Total Time

Work Done

The amount of work done is calculated as the product of work efficiency and time taken. The formula for work done:

Work Done = Work Efficiency x Time Taken

Rate Of Work

The rate of work refers to the speed at which work is being completed. It is calculated as 1 / Time taken for one unit of work.

Rate of Work = 1 / Time Taken

For instance, if a machine can complete a job in 6 hours, its rate of work is 1/6 jobs per hour. If it takes 3 days for 5 workers to finish a project, their combined rate of work is 5/3 projects per day.

Tips For Solving Time And Work Questions

Provided below are some of the tips for solving questions related to time and work:

Setting Equations

When approaching time and work problems, setting up equations accurately is crucial. Begin by defining variables for unknown quantities and translating the problem into mathematical expressions.

Step-By-Step Approach

Follow a systematic approach when solving time and work questions. Divide the work into parts based on the number of individuals or machines involved. Calculate individual rates to determine combined rates later.

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Time And Work Questions With Answers

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. Need to find out Vijay's work rate by subtracting Ajay's work rate from the combined work rate of Ajay and Vijay:

 V = 1/6 – 1/10 = 2/30 = 1/15

Vijay's work rate is 1/15. 

Let’s 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.

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 need 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 through 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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