# Time & Work Primer - Ravi Handa

• A work can be done by 4 people in 32 days. How many more days will it take if 16 people join them two days after starting?

In questions on 'Time and Work', it is a good idea to first calculate the total amount of work that is to be done. Often, you will find it terms of Man-Days.
In this particular question, we are given that 4 men take 32 days to complete the work
=> Total amount of work = 4 * 32 = 128 man-days
In the first two days, the 4 people will accomplish work worth = 4 * 2 = 8 man-days
Work remaining = 128 - 8 = 120 man-days
Total number of men that are now available to finish the work = 4 + 16 = 20 men
Number of days required by these men to finish the work = 120/20 = 6 days

6 men can do a piece of work in 30 days of 9 hours each, how many men will it take to do 10 times the amount of work if they work for 25 days of 8 hours?

Total amount of work that needs to be done = 6 men * 30 days * 9 hours = 1620 Man-Hours
10 times the amount of work would be 16200 Man-Hours
The men are now working for 25 days and 8 hours on each day
=> Every man is working for 25 * 8 = 200 hours
Number of men required = 16200 / 200 = 81 Men

A and B can finish a work together in 12 days, and B and C together in 16 days. If A alone works for 5 days and then B alone continues for 7 days, then remaining work is done by C in 13 days. In how many days can C alone finish the complete work?

Let us say that A takes 'a' days to finish the work, B takes 'b' days to finish the work and C takes 'c' days to finish the work.
=> A in one day will do 1/a units of work, and similarly B and C will do 1/b and 1/c units of work in one day.
We are given that A and B together can finish the work in 12 days
=> 1/a + 1/b = 1/12
Similarly, we are also given that B and C together can finish the work in 16 days
=> 1/b + 1/c = 1/16
We also know that the work can be finished if A works for 5 days, B for 7 Days and C for 13 days
=> 5/a + 7/b + 13/c = 1
So, we have three equations and three variables. We can solve them to get the individual values of 'a', 'b' and 'c'. We are asked to find out in how many days would C alone finish the work. So, we are asked to find out the value of 'c'.
If we multiply the first equation with 5 and the second equation with 2 and add them up, we will get
5(1/a + 1/b) + 2(1/b + 1/c) = 5/12 + 2/16
=> 5/a + 7/b + 2/c = (20 + 6)/48 = 26/48
=> 5/a + 7/b + 2/c = 13/24
If we subtract the above equation from the third equation, we will get
(5/a + 7/b + 13/c) - (5/a + 7/b + 2/c) = 1 - 13/24
=> 11/c = 11/24
=> c = 24
So, we can say that C alone will take 24 days to complete the work.

If 3 men completes work in 7 days how many days will 5 men take?

n this particular question, we are given that 3 men take 7 days to complete the work
=> Total amount of work = 3 * 7 = 21 man-days
We now have 5 men available with us.
Number of days required by these men to finish the work = 21/5 = 4.2 days

If 21 men take 30 days to a complete a work. In how many how days will 45 men complete the work?

In this particular question, we are given that 21 men take 30 days to complete a work
=> Total amount of work = 21*30 = 630 man-days
We now have 45 men available with us.
Number of days required by these men to finish the work = 630/45 = 14 days

Alex takes twice as much time as Andy and thrice as much as Viney to finish the work. Together they finish in 1 day. What is the time taken by Alex to finish the work?

Let us say that Viney takes '2x' hours to finish the work
=> Alex will take thrice as much, so Alex will take '6x' hours to finsih the work.
=> Andy will take half of what Alex takes, so Andy will take '3x' hours to finish the work.
Together, they finish the work in 24 hours.
=> 1/2x + 1/3x + 1/6x = 1/24
=> (3 + 2 + 1)/6x = 1/24
=> 1/x = 1/24
=> x = 24 hours = 1 day
Alex takes 6x hours or 6 days to finish the job.

A and B can complete a job in 30 and 20 days respectively. They start working together and B leaves 5 days before the work is finished. In how many days is the total work finished?

Method 1:
A and B can do the job in 30 and 20 days individually, so together they will take 30 * 20/(30 + 20) = 600/50 = 12 days.
The work that A can do in 5 days is 1/6th. So, A left when 5/6th of the work was done or A left after (5/6) * 12 = 10 days
Total time taken = 10 + 5 = 15 days.

Method 2:
A and B can do the job in 30 and 20 days. A worked for the complete period of 'd' days, whereas B worked for 'd-5' days to finish the job
=> d/30 + (d-5)/20 = 1
=> 2d + 3d - 15 = 60
=> 5d = 75
=> d = 15 days

Aslam, Zahid and Ali can do a work respectively in 15 days, 6 days and 10 days. How many days three men will spend together to finish three times that work?

In 1 day, working together they will do
1/15 + 1/6 + 1/10 = (2 + 5 + 3)/30 = 10/30 = 1/3 rd of the work
So, in 3 days they will finish the work.
To finish three times the work, they will need 3*3 = 9 days

Practice Questions:

Q1) Beginning with the second day, the amount of work Ram can do per day keeps doubling everyday he works. Sameer can always do the work done by Ram in 40% less time. Owing to this increasing ability, Sameer and Ram complete the job together in 2 days. How many days would it have taken if their efficiencies had remained constant?

Q2) It takes Bhuvan , Bheem and Bahadur 18, 24 and 36 days respectively to do a piece of work. Each of them does the same amount of work and they complete the work in 26 days. Instead if Bheem did extra work equal to sum of yth parts of the works done by Bhuvan and Bahadur, they could have completed the work one day earlier. How much more work did Bheem do in the second case as compared to that done by him in the first case?

Q3) A tank is full of water. A drain pipe , which can empty the full tank in 60 minutes, is opened . 18 minutes later another pipe which can fill the empty tank in 30 minutes is opened. After how much time , in total, is the tank full again(in minutes)?

Q4) The work done by Ananth in 12 hours is equal to work done by Anand in 15 hours, which in turn is equal to work done by Arjun in 20 hiurs. If working together they complete the work in 10 hours, in how many hours can each of them , working alone, complete the work?

Q5) A, B,C,D can do a piece of work in 8, 16,32,64 days respectively. D starts the work and C joins him after 1/4th of work is done. B joins them after half the work is done and A joins them after 3/4th work is done. How many days does it take to complete the work?

Q6) Twenty five persons start a job of digging over an area of 330 m2. From the second day, a new person joins the group each day. Each person digs 1m2 per day. Find the time taken to complete the job.

Q7) There is a water tank of capacity 1,000 L with two inlet pipes A and B that can pump in water at the rate of 50 L/hr and 25 L/hr respectively. An outlet pipe C attached to the tank can pump out water at the rate of 50 L/hr. Initially the tank is full and the outlet pipe is opened. Now when the water in the tank is (3/4)th of the maximum volume of water that it can hold, both the inlet pipes are opened until the tank becomes full after which they are closed back. This process is repeated for an infinite number of times. Find the volume of water in the tank as a fraction of the capacity of the tank after 205 hrs.

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