TIME & WORK

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GETTING STARTED

☛ If a person completes a work in X  days, then his /her one day work will be  1/X

Meaning, if his total work has X parts, he would have completed 1 out of those X parts, where X is the number of days.

Eg. If a person can complete a work in 12 days, he will complete 1/12th work in 1 day.

Conversely, if a day’s work of a person is 1/X , he will complete the work in X days.

Two People Working on a Job Together

Let us say, Ram completes a job in A days and Shyam takes B days to complete the same job.

The total time taken by them is calculated as follows:

Ram’s one day work = 1/A

Shyam’s one day work = 1/B

Total one day work = 1/A + 1/B = (A+B)/AB

Thus the work will be completed in AB/(A+B) days.

Eg. Bheem completes building a bridge in 4 days, and Hanuman completes building a bridge in 2 days. How many bridges will the complete together in 8 days?

Soln.

Bheem’s one day work = 1/4

Hanuman’s one day work = 1/2

Their one day work together = 1/4 + 1/2 = 3/4

Therefore, they take 4/3 days to construct one bridge together.

Considering that they have 8 days,

They will build 8/(4/3) = 6 bridges.

Concept of Man-Days

The product of men working on a job and the days taken to finish the job is known as ‘man-days’. 

SIGNIFICANCE:

This is the same concept as Inverse Proportion in Unitary Method. It is used to find the number of days 1 person will take to finish the job, given A people finish the job in X days.

If A people can complete a work in X no. of days, then one person will complete the work in AX of days.

Eg. Food supplies in fort guarded by 10 people will last for 10 days. If the no. of soldiers are increased to 25, how long will the supplies last?

Soln:.

The food supplies are available for 10 soldiers for 10 days.

 Let 1 soldier eat 1 unit of food every day, then there must be 10 x 10 =100 units of food in the fort.

If 1 soldier were to finish it, the food would last for 100 days.

Given that the no. of soldiers is increased to 25. Every day 25 units of food will be consumed in the fort.

Thus, the food will last for only 100/25 = 4 days.

Eg. If 10 persons can complete 2/3 rd task in 20 days, how long will the work be completed if 2 men were to complete the remaining task?

Soln:. Given that 2/3rd task is completed in 20 days, the task will be completed in

 20x 3/2 = 30 days.

10 men together can complete the task in 30 days.

If 1 man completes 1 unit of work a day, 300 units of work together form the task.

Already 2/3 x 300 units = 200 units of work are completed.

Remaining work = 100 units

2 persons will complete 2 units of work per day.

Thus, time taken to complete remaining work = 100/2

= 50 days

PIPES & CISTERNS

The pipes and cisterns problems are very similar to the time and work problems

☛If a tap can fill a tank alone in X hours, in 1 hour it will fill 1/X of the tank.

Eg. If a tank is filled by a tap in 2 hours, then in first hour, 1/2 of the tank will be filled.

The other half of the tank will be filled in the second hour.

 If two taps are opened at the same time and one tap fills the tank in X hours while the other tap fills the tank in Y hours. Time taken to fill the tank will be 

     =      XY/(X+Y) hours.

Here both the taps are doing the work of filling up the tank.

Eg. If one tap fills the tank in 8 hours while the other tank fills the tap in 10 hours. Find the total time to fill the tank completely.

Soln:.

Tank filled in 1 hr = 1/8 + 1/10 = 18/80

Thus, the tank will be completely filled in 80/18 hours.

☛ If one cistern fills the tank in X hours while the other empties the tank in Y hours, the tank will be filled or emptied depending on the values of X and Y.

Eg. A tank is filled by a pipe in 3 hours while another tap, empties it in 5 hours. Will the tank be emptied or filled?

Soln:.

Here one tap is doing the work of filling the tank while the other tap is doing the work of emptying the tank.

Work done by filling tap in 1 hour =1/3

Work done by emptying tap in 1 hour = 1/5

Work done by filling tap > Work done by emptying tank in 1 hour. So, the tank will be filled

Had the time of emptying tap < Time to fill the tank, tank will be emptied.

In the example, total work done by both taps = 1/3 – 1/5 (Since one tap is filling and the other is working against it, ie. emptying)

Work done in 1 hour= 1/3 – 1/5 = 2/15

Therefore, work will be completed (Tank will be filled) in 15/2 hrs = 7.5 hours.

PRACTICE PROBLEMS

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Created on By venkateshj

Time & Work - Concept Refresher

1 / 30

A and B together can complete a job in 24 days. B and C together can complete it in 24 days. A and C together can complete it in 20 days. Find the time taken by all of A, B and C to complete it.

2 / 30

Ajit and Baljit working together can complete a job in 20 days. Ajit alone can complete it in 30 days. Both work together for 10 days and then Baljit leaves. Find the time taken by Ajit to complete the remaining work.

3 / 30

A and B together can complete a job in 15 days A alone can complete it in 24 days. Find the time taken by B to complete it.

4 / 30

A and B can complete a job in 20 days and 30 days respectively. Find the time taken to complete it, if both A and B work together.

5 / 30

40 men take 20 days to complete a job working 9 hours a day. Find the number of men required to complete a job, thrice as large, in 30 days working 12 hours a day.

6 / 30

If 10 men take 30 days to complete a job, find the time taken by 40 men to complete it.

7 / 30

15 men take 30 days to complete a job working 10 hours a day. Find the number of days that 20 men will take to complete it if they work 15 hours a day.

8 / 30

P and Q together can complete a job in 16 days and 32 days respectively. They work on alternate days with P starting the job. In how many days will the job be completed?

9 / 30

P and Q together can complete a job in 4 days and 5 days respectively. They work on alternate days with Q starting the job. In how many days will the job be completed?

10 / 30

P and Q together can complete a job in 24 days and 48 days respectively. They work on alternate days with Q starting the job. In how many days will the job be completed?

11 / 30

A, B and C can complete a job in 12 days, 15 days and  10 days respectively. They work together and  complete it. If their total wage is  4800, find A’s wage.

12 / 30

Amar, Akbar and Anthony take a job on contract for Rs.1 lakh. Amar and Akbar started the job and completed  7/8 th of the work. Anthony then took over and completed the remaining work.  How much money will Anthony get?

13 / 30

Two men undertake a job for Rs.3600. They can complete it in 60 days and 30 days. They work along with a third man and take 15 days to complete it. Find the share that the third man should get.

14 / 30

P, Q and R can together earn Rs.50000 in 10 days. Q and R together can earn Rs 24300 in 9 days. P and R together can earn Rs.27200 in  8 days. Find R’s daily earning.

15 / 30

Machine A can make 1 lakh rotis in 12 hours. Machine B can make the same number of rotis in 10 hours while Machine C can make the same in 16 hours. All the machines are turned on  at 6 PM.  However machine B is turned off at 9 PM and the remaining two machines complete the work. At what time is the work completed?

16 / 30

A does 75% of a work in 30 days. He then calls in B and they together finish the remaining work in 6 days. How long B alone would take to do the whole work?

17 / 30

A can do a certain job in the same time in which B and C  can do it together. If A and B together could do it in 4 days and C alone in 12 days, then B alone could do it in:

18 / 30

A can do a piece of work in 10 hours; B and C together can do it in 6 hours 40 minutes, while A and C together can do it in 6 hours. How long will B alone take to do it?

19 / 30

If 2 men and 6 boys can do a piece of work in 12 days while 9 men and 9 boys can do the same in 4 days, the time taken by 8 men and 12 boys in doing the same type of work will be:

20 / 30

Ganesh, Gopal and Girish can complete a job in 20 days, 30 days and 24 days respectively. Ganesh works on all the days while Girish and Gopal help Ganesh on every third day. In how many days will the job be completed?

21 / 30

A can build a room in 16 days and B can do the same work in 12 days. C helps both of them to complete the job in 6 days. How much time will C alsone take to complete the work?

22 / 30

20 boys or 40 girls can complete a job in 30 days. Find the time taken by 10 boys and 30 girls to complete it.

23 / 30

A can complete a job in 18 days. He started the work and after 9 days, B joined him. They completed the job in 3 more days. Find the number of days in which B alone can complete it.

24 / 30

Ganesh is twice as good a workman as Kartik and takes 30 days less than the latter to complete a job. Find the time taken if both of them decide to do a task together

25 / 30

A and B can complete a job in 15 days and 25 days respectively. They started the work together, but due to an emergency B had leave after 5 days and A completed the work all alone. Find the total number of days taken to complete the work

26 / 30

Suresh takes thrice as much time as Shaam and five times as Iman to complete a job. Working together they complete the work in 4 days. In how many days can Shaam can alone complete the  work?

27 / 30

X and Y can complete a work together in 10 days. Y and Z can complete a work together in 12 days. If X, Y and Z all work together, they can complete the work in 6.66 days. In how much time will  X and Z working together, complete the same job?

28 / 30

P can finish a work in 36 days, Q in 18 days and R in 12 days. Q and R start the work but are forced to leave after 4 days. The remaining work was done by P in:

29 / 30

Sita and Gita together can do a piece of work in 15 days. Sita having worked for 8 days, Gita finishes the remaining work alone in 36 days. In how many days shall  Gita finish the whole work alone?

30 / 30

Ramesh and Suresh can do a work together in 12 days. Ramesh is 11/4 times as efficient as Suresh. How much time will Suresh alone take to complete the same work.

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