Time & Work

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TIME AND WORK

In these problems the number of persons, quantity of work done and time taken are important factors. Also time taken by a person depends on the efficiency of that person which comes into picture when different people do the work such as Women, children do the work alongside the men. The problems related to time and work can be solved by two major approaches – ratio & proportions and unitary method. Let us proceed to find some formulae related to these questions.

Important Formulas – Time and Work

If A can do a piece of work in n days, work done by A in 1 day = 1/n

If A does 1/n work in a day, A can finish the work in n days

If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can do W2 work in D2 days working H2 hours per day (where all men work at the same rate), then

M1 D1 H1 / W1 = M2 D2 H2 / W2

If A can do a piece of work in p days and B can do the same in q days, A and B together can finish it in pq / (p+q) days

If A is thrice as good as B in work, then

Ratio of work done by A and B = 3 : 1

Ratio of time taken to finish a work by A and B = 1 : 3

SOLVED EXAMPLES

Level 1

1. P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
A. 8/15	B. 7/15
C. 11/15	D. 2/11

Answer : Option A

Explanation :

Amount of work P can do in 1 day = 1/15

Amount of work Q can do in 1 day = 1/20

Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60

Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15

Fraction of work left = 1 – 7/15= 8/15

2. A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. B alone can complete the work in — hours.
A. 12 hours	B. 6 hours
C. 8 hours	D. 10 hours

Answer : Option A

Explanation :

Work done by A in 1 hour = 1/4

Work done by B and C in 1 hour = 1/3

Work done by A and C in 1 hour = 1/2

Work done by A,B and C in 1 hour = 1/4+1/3 = 7/12

Work done by B in 1 hour = 7/12 – 1/2 = 1/12

=> B alone can complete the work in 12 hours

3. A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?
A. 37 ½ days	B. 22 days
C. 31 days	D. 22 days

Answer : Option A

Explanation :

Work done by A in 20 days = 80/100 = 8/10 = 4/5

Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 — (1)

Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)

Work done by A and B in 1 day = 1/15 —(2)

Work done by B in 1 day = 1/15 – 1/25 = 2/75

=> B can complete the work in 75/2 days = 37 ½ days

4. P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. How many days does P alone need to finish the remaining work?
A. 8	B. 5
C. 4	D. 6

Answer : Option D

Explanation :

Work done by P in 1 day = 1/18

Work done by Q in 1 day = 1/15

Work done by Q in 10 days = 10/15 = 2/3

Remaining work = 1 – 2/3 = 1/3

Number of days in which P can finish the remaining work = (1/3) / (1/18) = 6

5. Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 110 pages?
A. 7 hour 15 minutes	B. 7 hour 30 minutes
C. 8 hour 15 minutes	D. 8 hour 30 minutes

Answer : Option C

Explanation :

Pages typed by Anil in 1 hour = 32/6 = 16/3

Pages typed by Suresh in 1 hour = 40/5 = 8

Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3

Time taken to type 110 pages when Anil and Suresh work together = 110 × 3 /40 = 33/4

= 8 ¼ hours = 8 hour 15 minutes

6. P works twice as fast as Q. If Q alone can complete a work in 12 days, P and Q can finish the work in — days
A. 1	B. 2
C. 3	D. 4

Answer : Option D

Explanation :

Work done by Q in 1 day = 1/12

Work done by P in 1 day = 2 × (1/12) = 1/6

Work done by P and Q in 1 day = 1/12 + 1/6 = ¼

=> P and Q can finish the work in 4 days

7. A work can be finished in 16 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is
A. 1:3	B. 4:3
C. 2:3	D. 2:1

Answer : Option B

Explanation :

Work done by 20 women in 1 day = 1/16

Work done by 1 woman in 1 day = 1/(16×20)

Work done by 16 men in 1 day = 1/15

Work done by 1 man in 1 day = 1/(15×16)

8. P,Q and R together earn Rs.1620 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?

A. Rs.40

B. Rs.70

C. Rs.90

D. Rs.100

Answer : Option B

Explanation :

Amount Earned by P,Q and R in 1 day = 1620/9 = 180 —(1)

Amount Earned by P and R in 1 day = 600/5 = 120 —(2)

Amount Earned by Q and R in 1 day = 910/7 = 130 —(3)

(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day

– Amount Earned by P,Q and R in 1 day = 120+130-180 = 70

=>Amount Earned by R in 1 day = 70
Ratio of the capacity of a man and woman =1/(15×16) : 1/(16×20) = 1/15 : 1/20

= 1/3 :1/4 = 4:3

Level 2

1. P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?
A. 10 days	B. 14 days
C. 15 days	D. 9 days

Answer : Option C

Explanation :

Amount of work P can do in 1 day = 1/20

Amount of work Q can do in 1 day = 1/30

Amount of work R can do in 1 day = 1/60

P is working alone and every third day Q and R is helping him

Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5

So work completed in 15 days = 5 × 1/5 = 1

Ie, the work will be done in 15 days

2. A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in – days if they work together.
A. 18 days	B. 22 ½ days
C. 24 days	D. 26 days

Answer : Option B

Explanation :

If A completes a work in 1 day, B completes the same work in 3 days

Hence, if the difference is 2 days, B can complete the work in 3 days

=> if the difference is 60 days, B can complete the work in 90 days

=> Amount of work B can do in 1 day= 1/90

Amount of work A can do in 1 day = 3 × (1/90) = 1/30

Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45

=> A and B together can do the work in 45/2 days = 22 ½ days

3. P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in
A. 30 days	B. 25 days
C. 20 days	D. 15 days

Answer : Option B

Explanation :

Work done by P and Q in 1 day = 1/10

Work done by R in 1 day = 1/50

Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50

But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as Work done by P in 1 day × 2 = 6/50

=> Work done by P in 1 day = 3/50

=> Work done by Q and R in 1 day = 3/50

Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25

So Q alone can do the work in 25 days

4. 6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in – days.

A. 4 days

B. 6 days

C. 2 days

D. 8 days

Answer : Option A

Explanation :

Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b

Work done by 6 men and 8 women in 1 day = 1/10

=> 6m + 8b = 1/10

=> 60m + 80b = 1 — (1)

Work done by 26 men and 48 women in 1 day = 1/2

=> 26m + 48b = ½

=> 52m + 96b = 1— (2)

Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200

Work done by 15 men and 20 women in 1 day

= 15/100 + 20/200 =1/4

=> Time taken by 15 men and 20 women in doing the work = 4 days

5. Machine P can print one lakh books in 8 hours. Machine Q can print the same number of books in 10 hours while machine R can print the same in 12 hours. All the machines started printing at 9 A.M. Machine P is stopped at 11 A.M. and the remaining two machines complete work. Approximately at what time will the printing of one lakh books be completed?
A. 3 pm	B. 2 pm
C. 1:00 pm	D. 11 am

Answer : Option C

Explanation :

Work done by P in 1 hour = 1/8

Work done by Q in 1 hour = 1/10

Work done by R in 1 hour = 1/12

Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120

Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60

From 9 am to 11 am, all the machines were operating.

Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60.

6. A can complete a work in 12 days with a working of 8 hours per day. B can complete the same work in 8 days when working 10 hours a day. If A and B work together, working 8 hours a day, the work can be completed in — days.
A. 5 ⁵⁄₁₁	B. 4 ⁵⁄₁₁
C. 6 ⁴⁄₁₁	D. 6 ⁵⁄₁₁

Answer : Option A

Explanation :

A can complete the work in 12 days working 8 hours a day

=> Number of hours A can complete the work = 12×8 = 96 hours

=> Work done by A in 1 hour = 1/96

B can complete the work in 8 days working 10 hours a day

=> Number of hours B can complete the work = 8×10 = 80 hours => Work done by B in 1 hour = 1/80

Work done by A and B in 1 hour = 1/96 + 1/80 = 11/480 => A and B can complete the work in 480/11 hours. A and B works 8 hours a day.

Hence total days to complete the work with A and B working together = (480/11)/ (8) = 60/11 days = 5 ⁵⁄₁₁ days

Pending work = 1- 37/60 = 23/60

Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11

which is approximately equal to 2. Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm

7. If daily wages of a man is double to that of a woman, how many men should work for 25 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.
A. 12	B. 14
C. 16	D. 18

Answer : Option C

Explanation :

Wages of 1 woman for 1 day = 21600/(40×30)

Wages of 1 man for 1 day = (21600×2)/(40×30)

Wages of 1 man for 25 days = (21600×2×25)/(40×30)

Number of men = 14400/(21600×2×25)/(40×30)=144/(216×50)/40×30)=144/9=16

8. There is a group of persons each of whom can complete a piece of work in 16 days, when they are working individually. On the first day one person works, on the second day another person joins him, on the third day one more person joins them and this process continues till the work is completed. How many days are needed to complete the work?
A. 3 ¹⁄₄ days	B. 4 ¹⁄₃ days
C. 5 ¹⁄₆ days	D. 6 ¹⁄₅ days

Answer : Option C

Explanation :

Work completed in 1st day = 1/16

Work completed in 2nd day = (1/16) + (1/16) = 2/16

Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16

An easy way to attack such problems is from the choices. You can see the choices are

very close to each other. So just see one by one.

For instance, The first choice given in 3 ¹⁄₄

The work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16

The work done in 4 days = (1+2+3+4)/16 = 10/16

The work done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn’t it?

The work done in 6 days = (1+2+3+4+5+6)/16 > 1

Hence the answer is less than 6, but greater than 5. Hence the answer is 5 ¹⁄₆ days.

(Just for your reference, work done in 5 days = 15/16)

Pending work in 6th day = 1 – 15/16 = 1/16.

In 6th day, 6 people are working and work done = 6/16.

To complete the work 1/16, time required = (1/16) / (6/16) = 1/6 days.

Hence total time required = 5 + 1/6 = 5 ¹⁄₆ days

Work and Time

Work is the transfer of energy from one object to another. It is measured in joules (J). The amount of work done is equal to the force applied times the distance moved in the direction of the force.

Time is the indefinite continued progress of existence and events that occur in an apparently irreversible order from the past, present, and into the future. It is measured in seconds (s).

The relationship between work and time is that the more time you spend working, the more work you will do. This is because the amount of work done is equal to the force applied times the distance moved in the direction of the force. The longer you apply the force, the more distance you will move the object, and the more work you will do.

Work and Speed

Speed is the rate at which an object moves. It is measured in meters per second (m/s).

The relationship between work and speed is that the faster you work, the more work you will do. This is because the amount of work done is equal to the force applied times the distance moved in the direction of the force. The faster you apply the force, the more distance you will move the object, and the more work you will do.

Work and Efficiency

Efficiency is the ratio of the work output to the work input. It is a dimensionless quantity.

The relationship between work and efficiency is that the more efficient you are at work, the less work you will have to do. This is because the amount of work done is equal to the force applied times the distance moved in the direction of the force. If you are more efficient, you will be able to apply the same force over a longer distance, and therefore do more work.

Work and Wages

Wages are the payment that an employee receives for their work. It is typically measured in dollars per hour (\$/h).

The relationship between work and wages is that the more work you do, the more wages you will earn. This is because the amount of work done is equal to the force applied times the distance moved in the direction of the force. The more work you do, the more force you will apply, and therefore the more wages you will earn.

Work and Energy

Energy is the ability to do work. It is measured in joules (J).

The relationship between work and energy is that work is a form of energy. When you do work, you are transferring energy from one object to another. The amount of work done is equal to the change in energy of the object.

Work and Power

Power is the rate at which work is done. It is measured in watts (W).

The relationship between work and power is that power is equal to the work done divided by the time taken to do the work. The more power you have, the more work you can do in a given amount of time.

Work and Machines

A machine is a device that makes work easier or more efficient. Machines can be simple, like a lever, or complex, like a car.

The relationship between work and machines is that machines can help you to do more work with less effort. This is because machines can amplify force or distance. For example, a lever can amplify force, while a pulley can amplify distance.

Work and Force

Force is the push or pull that causes an object to move. It is measured in newtons (N).

The relationship between work and force is that work is done when a force is applied to an object and the object moves in the direction of the force. The amount of work done is equal to the force applied times the distance moved in the direction of the force.

Work and Displacement

Displacement is the change in position of an object. It is measured in meters (m).

The relationship between work and displacement is that work is done when a force is applied to an object and the object moves a distance. The amount of work done is equal to the force applied times the distance moved in the direction of the force.

Sure, here are some frequently asked questions and short answers about different topics:

Money:
- What is the best way to save money?
  - The best way to save money is to create a budget and stick to it. You should also try to cut back on unnecessary expenses.
- How can I make more money?
  - There are many ways to make more money. You could get a part-time job, start a side hustle, or invest in stocks or real estate.
- What is the best way to invest money?
  - There is no one-size-fits-all answer to this question. The best way to invest money depends on your individual circumstances and goals. However, some general tips include investing in low-cost index funds and diversifying your portfolio.
Health:
- How can I improve my health?
  - There are many ways to improve your health. You could eat a healthy diet, exercise regularly, and get enough sleep. You should also see your doctor for regular check-ups.
- What are some common health problems?
  - Some common health problems include obesity, heart disease, and diabetes. These problems can be caused by a variety of factors, including genetics, lifestyle choices, and environmental factors.
- How can I prevent health problems?
  - There are many ways to prevent health problems. You could eat a healthy diet, exercise regularly, and get enough sleep. You should also see your doctor for regular check-ups.
Relationships:
- How can I improve my relationships?
  - There are many ways to improve your relationships. You could communicate more effectively, spend more time together, and do things that you both enjoy. You should also be willing to compromise and forgive each other.
- What are some common relationship problems?
  - Some common relationship problems include Communication problems, trust issues, and financial problems. These problems can be caused by a variety of factors, including Stress, busy schedules, and different expectations.
- How can I resolve relationship problems?
  - There are many ways to resolve relationship problems. You could talk to your partner about the problem, try to see things from their perspective, and compromise. You should also be willing to forgive each other.
Career:
- How can I find a job?
  - There are many ways to find a job. You could search online job boards, Network with people in your field, or attend job fairs. You should also tailor your resume and cover letter to each job that you apply for.
- How can I be successful in my career?
  - There are many ways to be successful in your career. You could set goals, develop your skills, and network with people in your field. You should also be willing to take risks and learn from your mistakes.
- What are some common career problems?
  - Some common career problems include feeling stuck in your job, not being challenged, and not being paid enough. These problems can be caused by a variety of factors, including the economy, your skills, and your experience.
- How can I overcome career problems?
  - There are many ways to overcome career problems. You could talk to your boss about your concerns, look for a new job, or start your own business. You should also be willing to take risks and learn from your mistakes.

I hope this helps!

Sure, here are some multiple choice questions on the following topics:

A car travels 200 miles in 4 hours. What is the Average speed of the car?
(A) 50 miles per hour
(B) 100 miles per hour
(C) 200 miles per hour
(D) 400 miles per hour
A train travels 60 miles in 2 hours. What is the average speed of the train?
(A) 30 miles per hour
(B) 60 miles per hour
(C) 90 miles per hour
(D) 120 miles per hour
A plane travels 1,000 miles in 5 hours. What is the average speed of the plane?
(A) 200 miles per hour
(B) 400 miles per hour
(C) 600 miles per hour
(D) 800 miles per hour
A boat travels 20 miles in 1 hour. What is the average speed of the boat?
(A) 20 miles per hour
(B) 40 miles per hour
(C) 60 miles per hour
(D) 80 miles per hour
A bicycle travels 10 miles in 30 minutes. What is the average speed of the bicycle?
(A) 10 miles per hour
(B) 20 miles per hour
(C) 30 miles per hour
(D) 40 miles per hour
A person walks 2 miles in 30 minutes. What is the average speed of the person?
(A) 2 miles per hour
(B) 4 miles per hour
(C) 6 miles per hour
(D) 8 miles per hour
A car travels 100 miles in 2 hours. What is the distance traveled per hour?
(A) 50 miles per hour
(B) 100 miles per hour
(C) 200 miles per hour
(D) 400 miles per hour
A train travels 60 miles in 2 hours. What is the distance traveled per hour?
(A) 30 miles per hour
(B) 60 miles per hour
(C) 90 miles per hour
(D) 120 miles per hour
A plane travels 1,000 miles in 5 hours. What is the distance traveled per hour?
(A) 200 miles per hour
(B) 400 miles per hour
(C) 600 miles per hour
(D) 800 miles per hour
A boat travels 20 miles in 1 hour. What is the distance traveled per hour?
(A) 20 miles per hour
(B) 40 miles per hour
(C) 60 miles per hour
(D) 80 miles per hour
A bicycle travels 10 miles in 30 minutes. What is the distance traveled per hour?
(A) 10 miles per hour
(B) 20 miles per hour
(C) 30 miles per hour
(D) 40 miles per hour
A person walks 2 miles in 30 minutes. What is the distance traveled per hour?
(A) 2 miles per hour
(B) 4 miles per hour
(C) 6 miles per hour
(D) 8 miles per hour
A car travels 100 miles in 2 hours. What is the rate of speed?
(A) 50 miles per hour
(B) 100 miles per hour
(C) 200 miles per hour
(D) 400 miles per hour
A train travels 60 miles in 2 hours. What is the rate of speed?
(A) 30 miles per hour
(B) 60 miles per hour
(C) 90 miles per hour
(D) 120 miles per hour
A plane travels 1,000 miles in 5 hours. What is the rate of speed?
(A) 200 miles per hour
(B) 400 miles per hour
(C) 600 miles per hour
(D) 800 miles per hour
A boat travels 20 miles