Time and Work  
When we started TG.Com, we were clear that TG would write about quant and I about business schools (India and Abroad). And who would write about verbal? No clue. The admission process, the happenings at business schools, interviews and group discussions used to excite me more than anything else in CAT arena. But as I moved closer to digging more information about business schools, I realized that Indian business schools do not have a very transparent admissions process. As far as learning goes, I started feeling the stagnation. I was not seeing much growth in that area and I did not want to move to the GMAT arena when I had yet not explored the Indian exams to their full potential. Back then, my love for language was not at its peak but I thought verbal was where I could be. I do not know when I decided to step into CAT Verbal Forum but I just took the step. As I started working in the CAT Verbal Forum, I started connecting with students on both personal and professional level. Today, if I want to count how many thankyous TG and I have received in these two years, I think I would fail. From Indian B School Maven, I have become TotalGadha.Com's verbal instructor and International B School Maven. It has been a long journey and I can only smile when I look back today. TotalGadha.Com is slowly becoming everybody's website. More than anybody else, our students are becoming our strongest support. So far you have seen student contributions in the form of CAT articles, you have seen contributions in our CBT Club , and you have seen contributions in the form of blogs. Today we present you a contribution from our GMAT blog.
Sindhoor has contributed an article on 'How to prepare for GMAT Verbal Section' before as well but this time we wanted to give him a bigger exposure. TG has really grinded him in solving loads of questions and he has been continuously working on the article from past many days. Don't forget to say thank you to him.  Dagny Problems on Time and Work are a common feature in most of the standard MBA exams. If you are well versed with the basics and have practised these problems during your preparation, they give you an easy opportunity to score and also save time. Here, I will try and give you the basic fundas with the help of examples. Let us start with a very basic problem:
Problem 1: A takes 5 days to complete a piece of work and B takes 15
days to complete a piece of work. In how many days can A and B complete the
work if they work together? > A’s 1 day work = 15/5 = 3 units > B’s 1 day work = 15/15 = 1 unit >(A + B)’s 1 day work = 3 + 1 = 4
units (Note: You can assume work to be any number of
units but it is better to take the LCM of all the numbers involved in the
problem so that you can avoid fractions) >X can do 1 unit of work in 1 day >Y’s 1 day work = 9/3 = 3 units. A, B, C work together in the first 2 days Problem 4: Gerrard can dig a well in 5 hours. He invites Lampard and
Rooney who can dig 3/4th as fast as he can to join him. He also invites Walcott
and Fabregas who can dig only 1/5th as fast as he can (Inefficient gunners you
see ) to join him. If the five person team digs the same well and they start
together, how long will it take for them to finish the job? Remember that whenever there is money
involved in a problem, the money earned should be shared by people doing the
work together in the ratio of total work done by each of them. Again I will
explain this with the help of an example:
Pipes and Cisterns
Problem 9: There are three hoses, A, B and C, attached to a reservoir. A and B can fill the reservoir alone in 20 and 30 mins, respectively whereas C can empty the reservoir alone in 45 mins. The three hoses are kept opened alone for one minute each in the the order A, B and C. The same order is followed subsequently. In how many minutes will the reservoir be full?
Solution: These kinds of problems can be solved in the same way as we solve problems where one or more men are involved. A, B and C are equivalent to three people trying to complete a piece of work. The amount of work to be done would be the capacity of the reservoir. Lets assume capacity of the reservoir = W = 180 (LCM of 20, 30, 45) litres. A can fill the reservoir in 20 mins Þ In 1 min A can fill 180/20 = 9 L. B can fill 180/60 = 6 L in a minute. In one minute C can empty 180/45 = 4 L from the reservoir. 1^{st} Minute => A is opened => fills 9 L 2^{nd} Minute => B is opened =>fills another 6 L 3^{rd} Minute => C is opened => empties 4 L Hence every 3 minutes => (9 + 6 – 4 =) 11 litres are filled into the reservoir. So in 45 minutes (11 × 15 =) 165 litres are filled. In the 46^{th} minute A is opened and it fills 9 litres. In the 47^{th} minute B is opened and it fills 6 litres. Hence the reservoir will be full in 47 minutes. Problem 10: There is an empty reservoir whose capacity is 30 litres. There is an inlet pipe which fills at 5 L/min and there is an outlet pipe which empties at 4 L/min. Both the pipes function alternately for 1 minute. Assuming that the inlet pipe is the first one to function, how much time will it take for the reservoir to be filled up to its capacity? Solution: The work to be done = Capacity of reservoir = W = 30 litres 1^{st} Minute => inlet pipe opened => 5l filled 2^{nd} minute => inlet pipe closed; outlet pipe opened => 4l emptied In 2 minutes (5 litres 4 litres =) 1l is filled into the reservoir. It takes 2 minutes to fill 1l => it takes 50 minutes to fill 25 litres into the tank. In the 51^{st} minute inlet pipe is opened and the tank is filled.Problem 11: Sohan can work for three hours nonstop but then needs to rest for half an hour. His wife can work for two hours but rests for 15 min after that, while his son can work for 1 hour before resting for half an hour. If a work takes 50 manhours to get completed, then approximately how long will it take for the three to complete the same? Assume all of them all equally skilled in their work. (a) 15 (b) 17 (c) 20 (d) 24
Solution: W = 50 manhours Since all of them are equally skilled; in 1 hour they can do 3 manhours of work if no one is resting. It will take them 50/3 = 16.6 hours to complete the work if they work continuously. But, since they take breaks the actual amount of time would > 17 hours. Option (a) and (b) are ruled out. Now let us calculate the amount of work done in 20 hours. Sohan does 3 manhours in every 3.5 hours (because he takes rest for half an hour on the 4^{th} hour) In 20 hours (3.5 × 5 + 2.5) Sohan completes => 3 × 5 + 2.5 = 17.5 manhours  (1) His wife completes 2 manhours every 2.25 hours (because she rests on the 3^{rd} hour) In 20 hours (2.25 × 8 + 2) she completes => 2 × 8 + 2 = 18 manhours.  (2) Child completes 1 manhours every 1.5 hour. In 20 hours (1.5 × 13 + 0.5) he completes 1 × 13 + 0.5 = 13.5 manhours of work.  (3) Adding 1, 2 & 3 In approximately 20 hours 49 manhours will be completed; so the work can be completed in 20^{th} hour.

Re: Time and Work  
This article is really very helpful for preparing Time and Work topic . Hope to get few more such topics from the author in future. 
Re: Time and Work  
Great article.Thanks a lot. If u have more number of questions pls post.
Regards Sanjeeb 
Re: Time and Work  
nice article thank u so much problem 7 is bit problematic...4 or 7 hours a day work is carried out not clear 
Re: Time and Work  
Thanks Shivam and read the last line of problem 7 .. it says everyone works for 4 hours a day. 
Re: Time and Work  
Vishnu, I am happy you liked it ... hoping to see your article someday on TG 
Re: Time and Work  
Sanjeeb,I am short of good questions in this topic too .. but will try and see if I can post more .. or may be you can post any that you encounter during your preparation. 
Re: Time and Work  
Great Effort! Nice Article! Thanks  SE 
Re: Time and Work  
Awsome article Sir!! Thanks a ton.. Hope to get some more articles from you. Regards, Killer 
Re: Time and Work  
Thanks A Lot. I think that there is a typing mistake in answer 4. It will be 100/58 hours.

Re: Time and Work  
I agree with Jay . Day in problem 4 should be replaced by hour 
Re: Time and Work  
grt article dude,feelin so confident nw. just replace 180/60 wid 180/30 in prb 9,just a printin mistake. TG sir,expectin some challenging prbs frm u in this topic. thanks ayush 
Re: Time and Work  
too good boss..very helpful 
Re: Time and Work  
after this artice I am feeling lot more confident with time and work.....thanks a lot 
Re: Time and Work  
Hi Sindhoor, Great Article, thanks a lot. Personally I like this chapter a lot, could you please put some good quality questions here specific to Time & Work? Regards, Tuhin

Re: Time and Work  
Hi Sindhoor, Thanks for the article..............!!!!! Parag 
Re: joydeep  
Is the answer three?? 
Re: Time and Work  
Guyz, Try this problem. Its a good one ..

Re: Time and Work  
great work done sindhoor... hope to see some more articles like this from you in future... thanks a lot 
Re: Time and Work  
@ Sindhoor.. Nice article... Which problem you are talking about..?? 
Re: Time and Work  
Ans is 6 ?? 
Re: Time and Work  
the answer is 3... 
Re: Time and Work  
Great article... Kudos... Post more challenging problems on the topic.. Thanks, VIckram. 
Time and Work  
very nice artical. i learned a lot. i try to use it in each prob. thanx 
Re: Time and Work  
Thanks Kulvir, I was telling about the problem posted by joydeep only and 3 is the right answer

Re: Time and Work  
Thanks Shyam 
Re: Time and Work  
A can make 4 walls in 9 days... 
Re: Time and Work  
hi Thanks for the post . Nice fundas!!

Re: Time and Work  
hi joydeep, kindly provide a detailed solution of the above problem (wall construction prob) as i am unable to solve it. thanks. antriksh 
Re: Time and Work  
this article have some really tricky questions 
Re: Time and Work  
hi Sindhoor, wont the ans be true for all multiples of 3 (regarding the no of workers problem)... i think 6,9 would also be right... please correct if am wrong. 
Re: Time and Work  
Great work and an equally great method... thnk u 
Re: Time and Work  
I getting the concepts...but some more problems will strengthen our basics and acumen... PLEASE PROVIDE MORE PROBs ON IT. 
Re: Time and Work  
Hi, I had preconceived notion that Time and work is tedious.. but this article has made it simpler and lucid.. Thanks Hari 
Re: Time and Work  
Hi,
could you put some probems which involve persons with different capabilities... 
Re: Time and Work  
That was awesome!! Explained beautifully!! Thanks so much for the post Sindhoor. Nikhil 
Re: Time and Work  
Thank you very much for this article. Regard, pavan 
Re: Time and Work  
Boss, ans is 40 min but this can be obtained by back calculation from given ans only is there a better way to solve??? 
Re: Time and Work  
thank u tg sir for dis article loking forwards 4 more of ur noble work.have a great day ahead cheers abhishek 
Re: Time and Work  
Hi TG, Thank you, this artical is really good ... 
Re: Time and Work  
" n + n1 + n2 + ........ +1 = (2/3)*n " I dint get this step in the solution to joydeep's question.. Can u explain me why u equated these two terms?? 
Re: Time and Work  
Wonderful! a very good variety....please post some more such problems...thanks a lot!! 
Re: Time and Work  
hiii... can anyone explain me the problems where two or more people are included and they work on alternate days?? i am not able to solve this kind of problems.. please help me... 
Re: Time and Work  
hey nitin... it may feel like stupidity... but can u explain one thing.. total units of work is 31 ... then how did u find that they wud take 15 days to complete the work??? 
Re: Time and Work  
really a great work thank u so much sir keep updating these kind of works 
Re: Time and Work  
gud work... 
Re: Time and Work  
for example3. , how are we getting LCM to be 600????? 
Re: Time and Work  
Dear ramkrishna roy, The values in the problem are 15,2,10,40,75 so LCM ( 15,2,10,40,75 ) =600. Regards, Pavan. 
Re: Time and Work  
thanx 
Re: Time and Work  
it was really a very useful post for time and work preparation. 
Re: Time and Work  
Time and work articles is really good. Thank you very much for posting the article here 
Re: Time and Work  
great n summarized piece on Time and Work, TG can you please help us on logarithms topic too. Thanks!! 
Time and Work e book  
tg sir i have sent u cheque for TSD and geometry e book bt have stioll nt received .CAT is v ery near.pls help prateek 
Re: Time and Work  
great article ... after reading i realized how simple it will be with taking LCM ... thanks a lot guys 
Re: Time and Work  
thnx sindhoor awesome artical

Re: Time and Work  
Abhishek, The equation would be sth like this: 8x = 12x  10(1+2+...11) x= 165 
Re: Time and Work  
Yup Miti, u r correct 
Re: Time and Work  
prefect 
Re: Time and Work  
hi Kamal Sir, Please help me with the above question. 
Re: Time and Work  
thank you sir.....!! gr8 and laudable work. thanks a lot........!! 
Re: Time and Work  
cud anyone out here provide me the link to the Ratio and proportion forum. I can't find it. It would be of great help. thanx 
Re: Time and Work  
u r genius boss. Actually speaking u r total n we are gadhas.. thats our site. help us improve still more with concepts of deeper complexity.. 
Re: Time and Work  
thanx for the response but ans is given as 40/9 days. 
Re: Time and Work  
Thanks, now i got the answer Silly me 
Re: Time and Work  
A can do a piece of work in 8 days and B in 7 days. they work alternately but for equal time. when will they complete the work? 
Re: Time and Work  
Thank you TG sir 
Re: Time and Work  
hey this q can be dosne by following formula: MEN*DAYS= TOTAL WORK 1st of al calculate total work: 16men*12days=192*2=384 M*8=192 M=192/8 =24 men 