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Time and Work
by Sindhoor Grandhi - Thursday, 9 July 2009, 01:59 PM
  cat 2009 cat 2010 time and workWhen 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. smile- 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?

Standard Solution: Let us consider Work to be 1 unit. So if W = 1 Unit and A takes 5 days to complete the work then in 1 day A completes 1/5th  of the work. Similarly B completes 1/15th of the work.
If they work together, in one day A and B can complete (1/5 + 1/15 = 4/15) of the work. So to complete 1 unit of work they will take 15/4 days.      

New method: Let us assume W = 15 units, which is the LCM of 5 and 15.

Given that total time taken for A to complete 15 units of work = 5 days

--> A’s 1 day work = 15/5 = 3 units
Given that total time taken for B to complete 15 units of work = 15 days

--> B’s 1 day work = 15/15 = 1 unit

-->(A + B)’s 1 day work = 3 + 1 = 4 units
-->15 units of work can be done in 15/4 days.

Many solve Time and Work problems by assuming work as 1 unit (first method) but I feel it is faster to solve the problems by assuming work to be of multiple units (second method). This would be more evident when we solve problems which are little more complex than the above one.

Problem 2: X can do a work in 15 days. After working for 3 days he is joined by Y. If they complete the remaining work in 3 more days, in how many days can Y alone complete the work?

Solution: Assume W = 15 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 15 units of work in 15 days

-->X can do 1 unit of work in 1 day

(Note: If I had assumed work as 13 units for example then X’s 1 day work would be 13/15, which is a fraction and hence I avoided it by taking work as 15 units which is easily divisible by 15 and 3)
Since X worked for 6 days, total work done by X = 6 days 
× 1 unit/day = 6 units.
Units of work remaining = 15 – 6 = 9 units.
All the remaining units of work have been completed by Y in 3 days

-->Y’s 1 day work = 9/3 = 3 units.
If Y can complete 3 units of work per day then it would take 5 days to complete 15 units of work. So Y takes 5 days to complete the work.

Problem 3: A, B and C can do a piece of work in 15 days. After all the three worked for 2 days, A left. B and C worked for 10 more days and B left. C worked for another 40 days and completed the work. In how many days can A alone complete the work if C can complete it in 75 days?

Solution: Assume the total work to be 600 units. (LCM of all the numbers)
Then C’s 1 day work = 8 units.
-->(A + B + C)’s 1 day work = 40 units.

A, B, C work together in the first 2 days
-->Work done in the first 2 days = 40 × 2 = 80 units
C alone works during the last 40 days
-->Work done in the last 40 days = 40 × 8 = 320 units
Remaining work = 600 – (320 + 80) = 200 units
This work is done by B and C in 10 days.
-->(B + C)’s 1 day work = 20 units
-->A’s 1 day work = (A + B + C)’s 1 day work – (B + C)’s 1 day work = 40 units – 20 units = 20 units
-->A can do the work of 600 units in 30 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 tongueout) 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?

Solution:  Let the work be 100 units.
Gerrard’s 1 hour work = 100/5 = 20 units
Lampard and Rooney’s 1 day work = 3/4
× 20 = 15 units.
Fabregas and Walcott’s 1 day work = 1/5
× 20 = 4 units.
Þ In one day all five of them can do = 20 + 15 + 15 + 4 + 4 = 58 units of work. Hence they can complete the work in 100/58 days.

I hope you got the knack of it. Let us now see how to solve the second kind of problems in Time and Work – the MANDAYS problems.

In these kinds of problems we need to remember that the number of men multiplied by the number of days that they take to complete the work will give the number of mandays required to complete the work. The number of mandays required to complete a piece of work will remain constant. We will try and understand this concept by applying it to the next three problems.

A Very simple problem to start with:

Problem 5: If 10 men take 15 days to complete a work. In how many days will 25 men complete the work?

Solution: Given that 10 men take 15 days to complete the work. So the number of mandays required to complete the work = 10
× 15 mandays. So assume W = 150 mandays.

Now the work has to be done by 25 men and since W = 150 mandays, the number of days to complete the work would be 150/25 = 6 days.

Problem 6: A piece of work can be done by 8 boys in 4 days working 6 hours a day. How many boys are needed to complete another work which is three times the first one in 24 days working 8 hours a day?

Solution: Assume the first piece of work to be 8
× 4 × 6 = 192 boy-day-hours.
The second piece of work = 3 (The first piece of work) = 3
× 192 = 576 boy-day-hours. So W = 576 boy-day-hours.
If this work has to be completed in 24 days by working 8 hours a day the number of boys required would be 576/(24
× 8)  = 3 boys. 

Problem 7: X can do a piece of work in 20 days working 7 hours a day. The work is started by X and on the second day one man whose capacity to do the work is twice that of X, joined. On the third day another man whose capacity is thrice that of X, joined and the process continues till the work is completed. In how many days will the work be completed, if everyone works for four hours a day?

Solution: Since X takes 20 days working 7 hours a day to complete the work, the number of day-hours required to complete this work would be 140 day-hours. Like in the two problems above, this is going to be constant throughout. So, W = 140 day-hours.
Amount of work done in the 1st day by X = 1day
× 4 hours = 4 day-hours
2nd day, X does again 4 day-hours of work. The second person is twice as efficient as X so he will do 8 day-hours of work. Total work done on second day = 8 + 4 = 12 day-hours. Amount of work completed after two days = 12 + 4 = 16 day-hours.
3rd day, X does 4 day-hours of work. Second Person does 8 day-hours of work. Third person who is thrice as efficient as X does 12 day-hours of work. Total work done on 3rd day = 4 + 8 + 12 = 24 day-hours
Amount of work completed after 3 days = 16 + 24 = 40 day-hours
Similarly on 4th day the amount of work done would be 4 + 8 + 12 + 16 = 40 day-hours
Work done on the 5th day = 4 + 8 + 12 + 16 + 20 = 60 day-hours
Total work done after 5 days = 4 + 12 + 24 + 40 + 60 = 140 day-hours = W.
So it takes 5 days to complete the work.


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:

Problem 8: X can do a piece of work in 20 days and Y can do the same work in 30 days. They finished the work with the help of Z in 8 days. If they earned a total of Rs. 5550, then what is the share of Z?

Solution: Let work W = 120 units. (LCM of 20, 30 and 8)
X’s 1 day work = 6 units
Y’s 1 day work = 4 units
(X + Y + Z)’s 1 day work = 15 units.

So Z’s 1 day work = 15 – (6 + 4) = 5 units
In 8 days Z would have completed 5 units/day
× 8 days = 40 units of work
Since Z does 40/120 = 1/3rd of the work, he will receive 1/3rd of the money, which is 1/3 x 5550 = Rs. 1850.

 

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.

1st Minute => A is opened => fills 9 L

2nd Minute => B is opened =>fills another 6 L

3rd 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 46th minute A is opened and it fills 9 litres. In the 47th 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

1st Minute => inlet pipe opened => 5l filled

2nd 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 51st minute inlet pipe is opened and the tank is filled.


Problem 11:
Sohan can work for three hours non-stop 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 man-hours 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 man-hours

Since all of them are equally skilled; in 1 hour they can do 3 man-hours 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 man-hours in every 3.5 hours (because he takes rest for half an hour on the 4th hour) 

In 20 hours (3.5 × 5 + 2.5) Sohan completes => 3 × 5 + 2.5 = 17.5 man-hours ---- (1)

His wife completes 2 man-hours every 2.25 hours (because she rests on the 3rd hour)

In 20 hours (2.25 × 8 + 2) she completes => 2 × 8 + 2 = 18 man-hours. ---- (2)

Child completes 1 man-hours every 1.5 hour.

In 20 hours (1.5 × 13 + 0.5) he completes 1 × 13 + 0.5 = 13.5 man-hours of work. ------ (3)

Adding 1, 2 & 3

In approximately 20 hours 49 man-hours will be completed; so the work can be completed in 20th hour.

 

Re: Time and Work
by Rahul Shinde - Thursday, 9 July 2009, 04:42 PM
 

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
by sanjeeb panda - Thursday, 9 July 2009, 04:47 PM
 

Great article.Thanks a lot.smilesmile

If u have more number of questions pls post.

 

Regards

Sanjeeb

Re: Time and Work
by vishnu madhavan - Thursday, 9 July 2009, 05:41 PM
  Thankuuu soo much Sindhoor.Really nice article cool big grin

The concept of taking work as mulitple units is simplifying probs to a grt extent.Thankuu

Hope smeday, we chotta gadhas too will be providing quality stuff like dis to our gadha land.Thnku TG & Dagny Maam
Rgrds
Vishnu
Re: Time and Work
by shivam mehra - Friday, 10 July 2009, 11:15 AM
  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
by Sindhoor Grandhi - Friday, 10 July 2009, 11:28 AM
 

Thanks Shivam smile

and read the last line of problem 7 .. it says everyone works for 4 hours a day.

Re: Time and Work
by Sindhoor Grandhi - Friday, 10 July 2009, 11:32 AM
  Vishnu, I am happy you liked it ... hoping to see your article someday on TG smile
Re: Time and Work
by Sindhoor Grandhi - Friday, 10 July 2009, 11:49 AM
 

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
by Software Engineer - Friday, 10 July 2009, 12:54 PM
  Great Effort! smile Nice Article! smile smile


Thanks
- SE
Re: Time and Work
by the killer - Friday, 10 July 2009, 03:47 PM
  Awsome article Sir!!
Thanks a ton..smile
Hope to get some more articles from you.

Regards,
Killer
Re: Time and Work
by Jay Sampat - Friday, 10 July 2009, 04:44 PM
 

Thanks A Lot.

I think that there is a typing mistake in answer 4. It will be 100/58 hours.

 

Re: Time and Work
by Vivek Narain - Friday, 10 July 2009, 07:04 PM
 

U rock dude. The article is very helpful. Please post in some more problems, esp. on pipes n cisterns, and those like the last problem where a person takes a break while working...

Thanks a ton..

Re: Time and Work
by kat goel - Friday, 10 July 2009, 10:03 PM
  I agree with Jay . Day in problem 4 should be replaced by hour

Re: Time and Work
by ayush roy - Saturday, 11 July 2009, 12:38 AM
  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
by akash gupta - Saturday, 11 July 2009, 01:28 AM
  too good boss..very helpful
Re: Time and Work
by amit kheterpal - Saturday, 11 July 2009, 10:10 AM
 

nice work bro..can u give us article on tsd,percentages,profit n loss..these article help us lot n save our time..

sir/mam/se/sindhoor

   can u make article on each n every topic..n please post sum questions too..i love studying in this site..i have learnt many things here more than my coaching institute.At the same time iam sad today i got backlog in my 6thsem engineering exams my entire planning is now shatered.iam not able to understand wat i should do..

Re: Time and Work
by Puneet Aggarwal - Saturday, 11 July 2009, 07:30 PM
  after this artice I am feeling  lot more confident with time and work.....thanks a lot
Re: Time and Work
by Tuhin Banerjee - Saturday, 11 July 2009, 10:22 PM
 

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
by Parag Paratkar - Saturday, 11 July 2009, 11:38 PM
  Hi Sindhoor,

       Thanks for the article..............smile!!!!!

-Parag
Re: Time and Work
by joydeep sarkar - Sunday, 12 July 2009, 10:44 AM
  here is a problem...
A group of workers was put on a job. From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in two-third of the time. How many workers were there in the group?
Re: Time and Work
by harshhal bandekar - Sunday, 12 July 2009, 05:56 PM
 

Dear Sindhoor

Nice article on time & work

But I did not follow your third solution properly. I suppose whenever we take the lCM of the individual's working days we do it to calcualte the total workdone in units for ex. in the first problem total workdone is 15units.

But in third problem you have taken the LCM 15,10,40 2,75.Just want to know the logic behind it. Also Please clarify why you have taken the LCM of above nos when the work done by A,B,C is

A = 2 days

B = 2 days with A,B + 10 days with C = 12 days

C = 2 days with A,B + 10days with B + 40 days all alone = 52 days

Please clarify ...

Re: Time and Work
by Sindhoor Grandhi - Monday, 13 July 2009, 12:40 PM
 

Hi harshhal,

Sorry for the late reply ..

In problem 3: Whatever you assume Work as; remember that you need to divide it with 75 days(to find C's 1 day work) and 15 days( to find A+B+C's 1 day work). So it is enough to take W as the LCM of 75 and 15 which is 75.

Solve the problem with W=75 units and you will get the same answer. You need to take a mental note of what you would be dividing W with while you are solving the problem. Got it? Tell me frankly if you still have a doubt ..  

   

Re: joydeep
by Kulvir Singh - Monday, 13 July 2009, 12:52 PM
  Is the answer three??
Re: Time and Work
by Sindhoor Grandhi - Monday, 13 July 2009, 12:53 PM
 

Guyz,

Try this problem. Its a good one ..

 

Re: Time and Work
by Gaurav Mittal - Monday, 13 July 2009, 04:00 PM
  great work done sindhoor... hope to see some more articles like this from you in future... thanks a lot
Re: Time and Work
by Kulvir Singh - Tuesday, 14 July 2009, 11:57 AM
  @ Sindhoor..
Nice article...
Which problem you are talking about..??
Re: Time and Work
by Amar Kr Dubedy - Tuesday, 14 July 2009, 03:48 PM
  Ans is 6 ??
Re: Time and Work
by joydeep sarkar - Tuesday, 14 July 2009, 10:43 PM
  the answer is 3...
Re: Time and Work
by Vickram Asokan - Wednesday, 15 July 2009, 10:51 AM
  Great article...
Kudos... Post more challenging problems on the topic..

Thanks,
-VIckram.
Time and Work
by Shyam Manawat - Wednesday, 15 July 2009, 05:08 PM
 

very nice artical.

i learned a lot. i try to use it in each prob.

thanx

Re: Time and Work
by Sindhoor Grandhi - Wednesday, 15 July 2009, 05:46 PM
 

Thanks Kulvir, I was telling about the problem posted by joydeep only and 3 is the right answer smile  

 

Re: Time and Work
by Sindhoor Grandhi - Wednesday, 15 July 2009, 05:47 PM
  Thanks Shyam  
Re: Time and Work
by joydeep sarkar - Wednesday, 15 July 2009, 06:34 PM
  Two friends decide to work together and complete the construction of the four walls of a room which is in the shape of a square.however,as b fell sick,a started the work alone and completed the construction of one wall and took "t" hours more than what they would have taken if they had worked together.after this a left and b,working alone completed the construction of the second wall and took "(25/16)t" hours more than what they would have taken if they had worked together.Finally,both of them worked together and completed the remaining two walls.the construction of the four walls was completed in 121 days.

in how many days can b alone complete the construction of the four walls?

if a total of 3600 is paid for the entire work,what is the share of a??? 
Re: Time and Work
by Kulvir Singh - Thursday, 16 July 2009, 12:12 AM
  A can make 4 walls in 9 days...
Re: Time and Work
by jyoti verma - Friday, 17 July 2009, 12:12 AM
 

hi

Thanks for the post .

Nice fundas!!

 

Re: Time and Work
by antriksh agarwal - Friday, 17 July 2009, 04:27 PM
 

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
by kumar swambhu - Sunday, 19 July 2009, 10:16 AM
  this article have some really tricky questions
Re: Time and Work
by tarun bhavnani - Sunday, 19 July 2009, 01:21 PM
   ans is  ---> b can do it in 45 days....
sol.-->
say a can do wrk in l days and b can do it in m days...
both can do it in n days....
l-n=t and m-n = (25/16)t
and
l+m+n = 121*24     (converting days to hrs)

3 equations n 3 unknowns...solve..
enjoy..
Re: Time and Work
by Hemant Ahire - Sunday, 26 July 2009, 08:13 PM
 

X can do a piece of work in 20 days and Y can do the same work in 30 days. They finished the work with the help of Z in 8 days. If they earned a total of Rs. 5550, then what is the share of Z?
Please correct me if I m wrong.

1/20+1/30+1/Z = 1/8

1/Z = 1/8 - (50/600)

1/Z = 1/8 - 1/12

1/Z = 1/24

Therefore Z can do piece of work in 24 days. So the ration of X:Y:Zwill be 20:30:24. Therefore share of Z will be 5550*(12/37) = 1800.

Re: Time and Work
by cc6886 cc - Tuesday, 28 July 2009, 11:39 AM
  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
by Umang Mathur - Wednesday, 29 July 2009, 04:35 PM
  The solution to last problem seems problem specific. Had the total man-hours required to complete the  work were not 50 but some creepy number, then directly multiplying by a number, as in this case by 20, would not be easily possible, rather, we would have then used, hit and trial approach.

Please Correct me if I am wrong.

Regards
Umang
Re: Time and Work
by diptadeep banerjee - Wednesday, 29 July 2009, 10:22 PM
 

hi Hemant,

I think we need to consider the ratio of work done rather than the time taken in doing the work.. that's what i understand.

Can anyone tell me how to solve joydeep's first question please?

Re: Time and Work
by Ajaykumar Kamne - Thursday, 30 July 2009, 10:21 AM
  hey tarun,

I had a doubt in ur solution for the question with 4 walls.

1. as the room is a square, the amount of work reqd to do each of the wall would be equal.
2. and considering l,m,n to be the hours taken by a,b and a+b together to build one wall.
the equations would be,

l-n = t
m-n = 25t/16
and l+m+2n = 121*24 (not l+m+n = 121*24 , 2n because they build two walls together.)

I have a doubt in the third equation of your solution. Correct me if am wrong.

Re: Time and Work
by Ajaykumar Kamne - Thursday, 30 July 2009, 10:49 AM
  solution for joydeep's first question,

let n be the no. of persons working on first day, thn

no of persons working first day = n
no of persons working second day = n-1
no of persons working third day = n-2
hence no of persons working on nth day = 1

if all n persons kept working daily, thn it took (2/3)n days.

n + n-1 + n-2 + ........ +1 = (2/3)*n
using sum of arithmetic progressions and solving this

1/2[2*(a)+(N-1)(d)] = 2N/3
1/2[2*(1)+(n-1)(1)] = 2n/3
1/2[n+1]  = 2n/3
n+1 = 4n/3
hence n = 3

and no, n cannot be any multiple of 3 as can be seen here,
let x be 1,2,3..... anything
then our equation would become,
xn + xn-1 + xn-2 +.....+1 = (2/3)*xn and solving similarly
1/2[2*(a)+(N-1)(d)] = 2N/3, here N = xn
1/2[2*(1)+(xn-1)(1)] = 2(xn)/3
1/2[xn+1]  = 2xn/3
xn+1 = 4xn/3
xn = 3.
n = 3/x (not an integer)
Hence n can only take value 3

other ways of solving this problem are welcome... smile
Re: Time and Work
by brijesh jadav - Monday, 3 August 2009, 12:18 PM
  Great work and an equally great method... thnk u
Re: Time and Work
by manish kakati - Tuesday, 4 August 2009, 06:23 PM
 

I getting the concepts...but some more problems will strengthen our basics and acumen...

PLEASE PROVIDE MORE PROBs ON IT.

Re: Time and Work
by harsh Rana - Friday, 7 August 2009, 12:10 AM
  Wow......Awe-inspiring explanation about Time and Work Topic. As usual same like other covered topics on this site. I feel amazed whenever i read your topics here and you guys make me addicted of your marvellous site. This site really educate me for my MBA formulations. Just, a week before got to know about TathaGat and now it'll become my diurnal habbit of surfing on this website. Infact, i already send you a 1600/- cheque for CAT CBT membership and number system or geometry e-book. Hope you will respond ASAP.

Here, i want to share some of my opinion about your site. First of all, if you can put a chat box here so aspirants can easily interact with each other and discuss all there problem also. And, i think you guys are fantabulous so don't restrict or confine yourself with Management exams only. Provide new courses also because our society extremely required your kinf off mentors.

When i read your article about becoming teacher, i was filled with complete emotions because in this fast-paced country everyone run like rat and want to win the race. They all become so much self-interested and caught in this monetary-system.

In my point of view, Teachers and Soldiers are two field which are completely neglected by our youth.

I guess, enough for today keep post like this which arousing or holding the attention of people like me.

You guyz are so "OBAMA

Cheers
Re: Time and Work
by Prime Optimus - Wednesday, 12 August 2009, 12:11 AM
  Hi,

 I had pre-conceived notion that Time and work is tedious.. but this article has made it simpler and lucid..

Thanks
-Hari
Re: Time and Work
by punit badal - Wednesday, 12 August 2009, 03:16 PM
 

Hi,

 

could you put some probems which involve persons with different capabilities...

Re: Time and Work
by Nikhil Lingala - Thursday, 13 August 2009, 10:00 PM
  That was awesome!! Explained beautifully!!

Thanks so much for the post Sindhoor. smile

Nikhil
Re: Time and Work
by PAVAN C - Saturday, 15 August 2009, 08:14 PM
  Thank you very much for this article.

Regard,
pavan
Re: Time and Work
by manish kakati - Wednesday, 19 August 2009, 11:23 AM
 

Please this for me:

There’s a lot of work in preparing a birthday dinner. Even after the turkey is in the

oven, there’s still the potatoes and gravy, yams, salad, and cranberries, not to

mention setting the table.

Three friends, Asit, Arnold, and Afzal, work together to get all of these chores done.

The time it takes them to do the work together is six hours less than Asit would have

taken working alone, one hour less than Arnold would have taken alone, and half the

time Afzal would have taken working alone.

How long did it take them to do these chores working together?

1. 20 minutes 2. 30 minutes 3. 40 minutes 4. 50 minutes

Re: Time and Work
by kanwarjit chadha - Wednesday, 19 August 2009, 09:14 PM
  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
by abhishek tripathi - Friday, 21 August 2009, 02:27 AM
  thank u tg sir for dis article loking forwards 4 more of ur noble work.have a great day ahead cheers abhisheksmile
Re: Time and Work
by Ravi Babu Gudipudi - Friday, 21 August 2009, 03:16 PM
 

Hi TG,

Thank you,  this artical is really good ...

Re: Time and Work
by Netra Mehta - Saturday, 22 August 2009, 02:56 AM
  " n + n-1 + n-2 + ........ +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
by mitesh anand - Monday, 31 August 2009, 01:07 AM
  hi everyone,
the ans for joydeep's 2nd prob wud be--
b can complete in 45*4=180 days(only I think u might hav mistaken in writing hrs instead of dayz at sum places)
a-1/36,b-1/45
so a's share-(5/9)*3600=2000
Re: ajaykumar kamne
by mitesh anand - Monday, 31 August 2009, 01:22 AM
  frnd...I hop ki I will simplify ur sol little bit..
let work done by each prson on each day=1 unit
no. of prsons working on 1st day=n--workdone->n units
no. of prsons working on 2nd day=n-1--workdone->n-1 units
no. of prsons working on nth day=1--workdone->1 unit

equation becomes->
n + n-1 + n-2 + ..... +1=(2/3)[n+n+n...upto 'n' times]

[n(n+1)]/2=(2/3)n^2

4n^2=3n^2+3n

n^2=3n

n=0 or 3
discarding 0,ans wud b 3 men.

Re: Time and Work
by Etti R - Saturday, 5 September 2009, 01:20 AM
  Wonderful! a very good variety....please post some more such problems...thanks a lot!!
Re: Time and Work
by Priyesh Tungare - Saturday, 5 September 2009, 09:44 PM
  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
by nitin bhat - Saturday, 5 September 2009, 11:01 PM
  Hi Priyesh,
Problems that include 2 or more people can be solved in the similar fashion as you take the units of work.

Ex. A can finish a work in 10 days and B takes 15 days to complete the same work whereas C takes 25 days to do the same job. Find the number of days it takes to finish the job when:
a) A,B & C all work on alternate days

b)A&B work on the same day and C works the next day.

Soln.Let the total amount of work be 150 units(LCM of 10,15,25) then the respective units of works of A-15,B-10 and C-6.

a)Work completed 1st Day-15(Only A works) 2nd day-10(Only B works) 3rd day -6 (Only C works) so at the end of 3 days the amount of work finished-15+10+6=31Units.hence they would take Approx.15 days(14.51) to complete the work.

b)When A&B work same day the work completed-25 units on day 1 next day since only C works, units of work completed on day 2 is 6Units. So at the end of 2 days the unit of work completed is(25+6)=31Units. So to complete 150 units it'll take them Approx. 10 Days(9.61).

I hope you have understood by now....

Regards,
Nitin Bhat
nitinr.bhat@gmail.com
Re: Time and Work
by Priyesh Tungare - Saturday, 5 September 2009, 11:19 PM
  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
by nitin bhat - Sunday, 6 September 2009, 12:49 AM
  Priyesh,

3Days-31 Units of work done, next 3 days  62 units done, next 3 days 93 units done.... so on and so forth by the end of 15 days 155 units of work will be completed... our target is to complete 150 units of work.... so it'll be little less than 15 days...

Regards,
Nitin
Re: Time and Work
by sindhuja morampalli - Friday, 11 September 2009, 04:05 PM
 

really a great work

thank u so much sir

keep updating these kind of works

Re: Time and Work
by Neetendra Mishra - Sunday, 13 September 2009, 08:51 PM
  gud work...
Re: Time and Work
by ramkrishna roy - Thursday, 17 September 2009, 03:54 PM
  for example-3. , how are we getting LCM to be 600?????
Re: Time and Work
by PAVAN C - Tuesday, 22 September 2009, 12:31 AM
  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
by devesh bhattacharya - Friday, 25 September 2009, 07:06 PM
  I tried the approach its wonderful.
i tried a few more questions of different variety and placing them heresmile

Q1>

if 20 men or 24 women or 40 boys can do a work in 12 days working for 8 hours a day, How many men working with 6 women and 2 boys take to do a job 4 times larger, if they work 5 hours a day for 12 day?

STOP HERE first try it do by yourself.
if u can't solution is here.


Solution:
take lcm as 480.
total work hours for 1st job is 12*8= 96 man hours.
now every group here takes 96 man hours, so,
first group of men will do 480/96 = 5 units of work per hour.
Same is true for group of women and boys.


each man will do 5/20 unit work per hour.
each Women do 5/24 unit work per hour,
each boy will do 5/40 unit per hour.


now the new task is 4 times bigger i.e 480*4 units.

now equate
let no. of men working on new task be = x
no. of women working are 6
no. of boys working = 2

now x*(5/20)+ 6*(5/24) + 2*(5/40) = 480 * 4

it gives x = 122
which is the no of men required.
enjoysmile


Re: Time and Work
by jaya dulani - Thursday, 1 October 2009, 03:32 PM
 

Awesome article smile!!!!

U've made time & work probs much easier and interesting for me..

Thanks a ton!!!

@Tarun- hey tarun, i agree with Ajay..shudn't that be 2n, as both of them constructed two walls together. Moreover, aren't there 4 unknowns and 3 equations? Plz lead me to the correct solution. Thanx..

Re: Time and Work
by arpita bansal - Saturday, 3 October 2009, 10:27 AM
 

can someone please help me in solving this question:

a large tank of height 10m is fitted with an inlet which can fill it in 60 minutes. the tank has 3 outlet pipes fitted at the heights of 5m, 8m, 9.5m, from the bottom. all the pipes are opened simultaneously, with the tank being empty initially. in how much time 95% of the tank can be filled? if the outlert pipe can empty half of the tank in 1 and half hours,  the outlet pipe in the middle can empty 20% of the tank in 1 hr 12 min and outlet pipe at the top can empty 5% of teh tank in 18 mins

Re: Time and Work
by arnab das - Tuesday, 6 October 2009, 01:32 PM
 

it's very helpful. Thanks a lot.

It will be very good if you can kindly can upload an article based on time and distance(Mainly circle problem, A,B, C running and how many times they meet, kinna........)

It will be very helpful if you do so.....

Re: Time and Work
by supriya naidu - Thursday, 8 October 2009, 12:34 PM
  Hi

Thanks for  the information.I have found one site snapwiz.co.in  there is lot of good stuff regarding this chapter in case if you are planning to prepare as a whole for CAT  i strongly recommend you to look snapwiz .Take the tests there and compare your percentile score with respective to each subject. Now a days there is promotional offer going on.i registered through promotional code SW100CAT
you can also try this
Re: Time and Work
by Prudhvi G - Thursday, 8 October 2009, 04:38 PM
  Q1> by Devesh
If 20 men or 24 women or 40 boys can do a work in 12 days working for 8 hours a day, How many men working with 6 women and 2 boys take to do a job 4 times larger, if they work 5 hours a day for 12 day?

Alternate solution for this problem:

Work = 12 D X 8 H = 96 Day-Hours
As a group of 20 Men or  24 Women or 40 Boys can do the work in same time
 20 M = 24 W = 40 B
  5 M  =  6 W  = 10 B   (please do not blame me for gender bias -))

Work = 12 x 8 x 20  man-day-hours
New work = 4 x previous work = 4 x (12 x 8 x 20 ) M-D-H
Let the new work be done by Men alone.
New work done by: 6 W + 2 B + a M => 5 M + 1M + a M (relation btw M,W,B )
New work = 4 x (12 x 8 x 20 ) = (5+1+a) x 5 x12
a = 128 - 6 = 122 men
 
~Cheers~
Raj
Re: Time and Work
by sushil krishna - Saturday, 10 October 2009, 03:09 AM
  thanx
Re: Time and Work
by manish majumder - Monday, 12 October 2009, 07:07 PM
 

it was really a very useful post for time and work preparation.

Re: Time and Work
by VENU REDDY - Wednesday, 21 October 2009, 11:24 AM
  Time and work articles is really good. Thank you very much for posting the article here
Re: Time and Work
by Pankaj Kumar - Thursday, 29 October 2009, 01:02 PM
  great n summarized piece on Time and Work, TG can you please help us on logarithms topic too.

Thanks!!
Re: Time and Work
by smriti chhabra - Wednesday, 4 November 2009, 10:53 AM
  hi! ds article s really helpful! plz gve such articles n all important topics n CAT! but i ve sme doubts in problem 9 ve understood upto dt levet dt 11 litres are filled into d reservior after dt last 2 steps plz make me understand n problem 3 too!
Time and Work e book
by prateek bansal - Tuesday, 10 November 2009, 02:15 AM
  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 e book
by jatin arora - Tuesday, 10 November 2009, 12:50 PM
 

Dear Sir ,

the problems can also be solved using work efficiences also

1. A does work in 5 days so A eff% = 100/5

    B does work in 15 days so B eff% = 100/15

    Eff% of A + Eff% of B = 100/5 + 100/15 = 400/15

    Both can A and B can do work in = 100/400/15

                                                = 15/4 answer

 

2. A does work in 15 days so A eff% = 100/15=20/3

     A works for 6 days

    so work completed by A in 6 days = (20/3)*6 = 40%

   so work to be completed by B in 3 days = 60%

   B eff% = 60/3 = 20%

So B alone can do work in = 100/20

                                      = 5 days       answer

                     

Re: Time and Work
by Samit Katiyar - Monday, 16 November 2009, 09:34 PM
 

Hello Sir...

 

Many many thanks to u............In Quant,Time and Work was the only section where I have solved any question correctly..........But after going through ur solving  skills.........I can solve TnW questions............Thanks a lot for this great tutorial.......... 

Re: Time and Work
by Ankit Garg - Tuesday, 24 November 2009, 11:12 AM
  great article ... after reading i realized how simple it will be with taking LCM ... thanks a lot guys 
Re: Time and Work
by nidhi soni - Sunday, 29 November 2009, 05:27 PM
 

thnx sindhoor smile awesome artical smile

 

Re: Time and Work
by abhishek rai - Tuesday, 8 June 2010, 04:31 AM
  I may be an idiot, but please see the following.

A group of men decided to do a job in 8 days. But since 10 men dropped everyday, the job got completed in 12 days. How many men were at the beginning?

I got the answer as 330. Am I correct. I think the answer, given as 165 is wrong..Help!!!
Re: Time and Work
by Gul Gul - Tuesday, 8 June 2010, 08:58 AM
  Abhishek,

The equation would be sth like this:

8x = 12x - 10(1+2+...11)

x= 165
Re: Time and Work
by abhishek rai - Tuesday, 8 June 2010, 01:49 PM
  Thnx Gulab...

But accroindgly, 660 men dropped in 12 days, but only 165 men were at the begining!!!!! Shouldn't the no. of dropped people be 110.

Then,

8x=(x-110)*12
or, 8x = 12*110-12x
or, 4x=12*110
or x= 330.

Now plz explain!!!

also, initially, the no. of mandays required 1320, if 165 is the answer and after after dropping of 110 people, it becomes 540. Something fishy!
Re: Time and Work
by miti chakraborty - Tuesday, 8 June 2010, 02:29 PM
 

ajay,

i used simple trial nd error method 2 solve dis q...

here, t1/t2= 1/(2/3) = 3/2

therefore, w1/w2= 2/3

nw capacity of each person is same. Let us assume capacity is x for all.

nw using trial nd error....

w1= 3x+2x+x=6x

w2= 3x+3x+3x = 9x

w1/w2=2/3

i knw, it cant b d proper way 2 solve ds q...but it's time saving...

Re: Time and Work
by miti chakraborty - Tuesday, 8 June 2010, 02:56 PM
 

abhisek,

the no. of men dropped during the process is :-

o for the 1st day

10 for the (2nd, 3rd, 4th, 5th, ........, 12th day)

i.e. in total (10 X11)= 110 men were dropped according to the q

am i right, gulab????

 

Re: Time and Work
by Gul Gul - Tuesday, 8 June 2010, 08:53 PM
  Yup Miti, u r correct smile
Re: Time and Work
by umang shastri - Thursday, 2 September 2010, 03:14 PM
  prefectsmile
Re: Time and Work
by Mohit Sharma - Tuesday, 3 April 2012, 09:58 AM
  @ joydeep,
Let both the frnd can complete the wrk in X hrs,
then, first frnd can complete wrk in= X+t hrs
second frnd can complete wrk in= X+25t/16,

We also knw that,
1/X=1/(X+t)+1/(X+25t/16)
from this we get,
4X=5t
Now use,
(X+t)+(X+25t/16)+2X= 121*24 hrs
and calculate the value of X and t.
Re: Time and Work
by Mohit Sharma - Thursday, 5 April 2012, 10:27 PM
  Hi Kamal Sir,
Please help me with the question.

Ques: Mini and Vinay are quiz masters preparing for a quiz. In x minutes, Mini makes y questions more than Vinay. If it were possible to reduce the time needed by each to make a question by two minutes, then in x minutes Mini would make 2y questions more than Vinay. How many questions does Mini make in x minutes?
a) 1/4[2(x+y)-sqrt(2x^2+4y^2)]
b) 1/4[2(x-y)-sqrt(2x^2+4y^2)]
c) Either a or b
d) 1/4[2(x-y)-sqrt(2x^2-4y^2)]
e) None of these
Re: Time and Work
by Mohit Sharma - Wednesday, 18 April 2012, 06:52 PM
  hi Kamal Sir,
Please help me with the above question.
Re: Time and Work
by Kirti Sahoo - Wednesday, 6 June 2012, 10:31 AM
  Hello TG,
I think there's a bit of an anomaly in the solution for Problem 4.
In the solution it's given that Lapmpard and Rooney's 1 day work = 15 units but i think it should be 1 hours work and same with Fabregas and Walcott.
So there combined 1 hours work should be 39 units and thus they can complete the work in 100/39 hours or 2.56 hrs

As per the solution provided here the answer 100/58 days is absurd because that's approx. 1.72 which is greater than 1 day which can't be the case as Gerrard himself takes 5 hours to complete the work so with the help of 4 other people he should be able to complete the work in less time.

Please check the solution and correct me if i'm wrong. smile

Thanks.
Re: Time and Work
by kirti vardhan - Sunday, 29 July 2012, 04:39 PM
  my first post on TG:

There is another concept that can be used to solve time work problems and that is the FRACTION RULE. I will post a question here.i will give you the easy method.

25 men and 20 days to construct a 10 mt wall.how many men are required to make an 8 mt wall if it is planned that the work be completed in 10 days..

FRACTION RULE:
take the value of the quantity that is to be calculated as reference..here 25.

then frame the fractions by the following:

if number of days decreases (20 to 10) the number men has to inclrease so the fraction that has to be multiplied should be
greater than 1 so 20/10.

next for constructin an 8 mt wall lesser number of men are required as compared to a 10mt wall so the fraction has to be less than 1 i.e. 8/10

so men required = 25*(20/10)*(8/10)= 40 men(answer)

hope this helps u to crack questions faster.
Re: Time and Work
by Pratibha B - Friday, 3 August 2012, 11:17 AM
  Sindhoor,

I have a confusion in problem No.7.

The question says "everyone works for four hours a day". I don't understand why, then, other workers apart from X work more than four hours a day[as per the solution].

Please clarify.

Re: Time and Work
by Rhythm Goyal - Sunday, 5 August 2012, 10:57 PM
 

HI Hemant,

Z alone "can do" work in 24 days. But he worked only 8 days.

Also payment does not depend on number of days worked for, but on the amount of work.

Thus in 8 days he worked 1/24*8 part of work i.e. 1/3 of work.thus payment too 1/3rd only.

Re: Time and Work
by sameer sapre - Sunday, 5 August 2012, 11:17 PM
  thank you sir.....!!
gr8 and laudable work. thanks a lot........!! smile smile
Re: Time and Work
by Ashwani Kushwaha - Friday, 24 August 2012, 03:23 PM
  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
by anil mosali - Monday, 10 September 2012, 07:43 AM
  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..smile
Re: Time and Work
by jyotsna chauhan - Monday, 22 October 2012, 09:00 PM
  hello Sindhoor,
 Please solve this question for me . Thank you.
Four pipes can fill a reservoir in 15, 20,
30 and 60 hours respectively. The first
one was opened at 6 AM, second at 7
AM, third at 8 AM and the fourth at 9
AM. When will the reservoir be filled ?
Re: Time and Work
by vivek 231 - Tuesday, 23 October 2012, 04:27 PM
  hi

let the capacity of tank be 60 (l.c.m of 15,20,30,60)

and the pipe A will fill at a rate 4 litres per hour

B at 3,c at 2 AND D AT 2,

in the first hour only A is opened so 4litrs will be filled

in the second A and B so 7

in the third hour a,b,and c 9

in the fourth a,b,cand D 10

now 30 litres will be filled at 10a.m after that it will take
3 hours to fill (30/(4+3+2+1)=3hours) ,

so it will be filled completely at 12.00
Re: Time and Work
by ankit SAHAY - Sunday, 8 September 2013, 10:18 PM
  hi,
can some one please solve this question:

The rates at which Alok and Bhaskar work are in the ratio 5 : 4. They work on alternate days to complete a job. Bhaskar started the job and he worked on the last day. The job was completed in 1 day more than the time that Alok alone would take to complete it. Find the time taken (in days) by them working together to complete the job.
Re: Time and Work
by debaditya khan - Monday, 9 September 2013, 01:43 PM
  Efficiency of A: B= 5:4
let total work is 100x
total wok=(5+4)x=9x
now total work=9x*11=99x( in 22 days)
in 23 days the rest work i,e. x will be completed by B @(x/4x)

therefore total work will be completed in 23 days.
Re: Time and Work
by ankit SAHAY - Monday, 9 September 2013, 07:31 PM
  thanx for the response but ans is given as 40/9 days.
Re: Time and Work
by rimmi rimmi - Saturday, 19 April 2014, 06:17 PM
  For Problem 7:

Please tell me whats wrong in this solution:

Let x be the total days taken for work done.

A worked for x days
B worked for x-1 days
C worked for x-2 days

1 day work for A for 4 hrs: 4x/20*7
1 day work for B for 4 hrs: 2*4(x-1)/20*7
1 day work for C for 4 hrs: 3*4(x-2)/20*7

Now, the addition of above three eqns should be 1

So, 4x/20*7 + 2*4(x-1)/20*7 + 3*4(x-2)/20*7 = 1

and x=43/6

Please let me know, what's wrong in this???????? smile
Re: Time and Work
by TG Team - Monday, 21 April 2014, 04:35 PM
  Hi Rimmi smile

You missed in the question that "the process continued after that.." i.e. after third day too new workers are being added everyday. Please re-read the question statement.

Kamal Lohia
Re: Time and Work
by rimmi rimmi - Saturday, 26 April 2014, 01:05 AM
  Thanks, now i got the answer smile
Silly me mixed
Re: Time and Work
by kshitiz regmi - Monday, 5 May 2014, 05:35 PM
  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
by TG Team - Tuesday, 6 May 2014, 06:17 PM
  Hi Kshitiz smile

What's the difficulty you are facing in this?

Just assume the total amount of work to be done is LCM(8, 7) = 56 units which A can finish in 8 days i.e. 56/8 = 7 units daily, and B can finish in 7 days i.e. 56/7 = 8 units daily.

Now just count the amount of work finished each day as both of them are working on alternate days.

Hope it helps.

Kamal Lohia
Re: Time and Work
by Abheek Das - Sunday, 3 August 2014, 02:47 PM
  In Problem 4:

When we find out that Lampard and Rooney complete 15 units in one day together.
How can we say that individually Lampard and Rooney work 15 units?
Shouldn't the work of the five individuals be:
Gerrard + Lampard +Rooney+ Fabrigas+Walcott= 20+15+4= 39 units
How does this become 58 units?
Re: Time and Work
by Abheek Das - Sunday, 3 August 2014, 03:09 PM
  A & B are working on a job.A is the builder and B is the demolition man.A takes 10 days to construct a wall completely.B takes 20 days to demolish it completely.How much time do they take to build a wall completely?

If they work on alternate days and A starts the job.
Re: Time and Work
by Akhilesh Beri - Monday, 4 August 2014, 08:03 PM
 

Please clarify on the point in Problem 4:

1. He invites Lampard and Rooney who can dig 3/4th as fast as he can to join him.

=> Lampard and Rooney can complete work at speed of  20 units/hr + 3/4(20)= 35 units/hr

Similarly for next it should be 24 units/hr

Hence total time would be 100/ 79 hours.

Please check & confirm.

Re: Time and Work
by TG Team - Tuesday, 5 August 2014, 01:36 PM
  Hi Abheek smile

It's for the individuals not the pairs. Lampard and Rooney completes 15 units each and Fabrigas and Walcott completes 4 units each in same time when Gerrard completes 20 units.

I hope it is clear now. smile

Kamal Lohia 
Re: Time and Work
by TG Team - Tuesday, 5 August 2014, 01:40 PM
  Hi Akhilesh smile

"3/4th as fast as he can" means 3/4th of speed of Gerrard and not 3/4th more than speed of Gerrard.

Also the statement about speeds is true for each of the persons and not in the pairs as you have assumed it.

Hope it helps. smile

Kamal Lohia
Re: Time and Work
by Mr. Daemon - Saturday, 6 September 2014, 11:14 PM
  I have a question, Suppose that ratio of efficiency of A and B are 2:1  . and Difference between their efficiencies i.e A-B = 1/15 .

Now I can of-course punch in the value of ratio like 2x-1x = 1/15 and x= 1/15 , putting back the value of x in the ratio , which is A = 2/15 and B =1/15 i.e  A takes 15/2 days and B takes 15 days .

But we know efficiency is inversely proportional to time , Hence time ratio of A and B  =  1 : 2 . Now comes my confusion, What I was thinking to do is ,
Initially I had A-B = 1/15 (diff. of efficiencies, see first para) , I can inverse it, which says Difference of time taken by A and B = 15 days.

now putting the value of ratio of A:B (days) 2x-x =15 , hence x=15 , which says A takes 15 days and B takes 30 days . Now where my logic goes wrong?

Thanks a lot smile
Re: Time and Work
by A ghosh - Sunday, 26 October 2014, 10:45 PM
  Hi, tat article really helped a lot,thanksss smile could you please explain how do we do the following ques ?
A dam has 4 inlets. thru the first 3 inlets, the dam is filled in 12 mins, thru the 2nd ,3rd and 4th inlet, in 15 min. thru the 4th inlet in 20 mins. how much time will it take all the four inlets to fill the dam?
Thanks in advance !
Re: Time and Work
by lemba leichombam - Tuesday, 28 July 2015, 09:00 AM
  please solve this..Q. 16 men are employed to do a work in 20 days. at the end of 12 days the work is only half done . how many additional number of men should be employed to complete the work in the stipulated time?
Re: Time and Work
by pawan rawat - Monday, 17 August 2015, 11:58 AM
  A and B can do a work in 30 days .B and C can do it in 20 days.A starts the work and works for 5 days then B takes the work and works for 15 days .finally C finishes the work in 18 days.the no of days in which C alone can do the work doing it separately.
Re: Time and Work
by Sandesh Naik - Tuesday, 24 November 2015, 02:58 PM
  Thank you TG sir smile
Re: Time and Work
by Pradeep Sharma - Thursday, 24 December 2015, 01:41 PM
  It takes 6 days for 3 women and 2 men to complete. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a men exceed that of a woman.
Plz answer in 1/n type method
Re: Time and Work
by Pradeep Sharma - Thursday, 24 December 2015, 01:55 PM
  It takes 6 days for 3 women and 2 men to complete. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a men exceed that of a woman.
Plz answer in 1/n type method
Re: Time and Work
by Pradeep Sharma - Thursday, 24 December 2015, 01:55 PM
  It takes 6 days for 3 women and 2 men to complete. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a men exceed that of a woman.
Plz answer in 1/n type method
Re: Time and Work
by Pradeep Sharma - Thursday, 24 December 2015, 01:55 PM
  It takes 6 days for 3 women and 2 men to complete. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a men exceed that of a woman.
Plz answer in 1/n type method
Re: Time and Work
by Pradeep Sharma - Thursday, 24 December 2015, 01:55 PM
  It takes 6 days for 3 women and 2 men to complete. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a men exceed that of a woman.
Plz answer in 1/n type method
Re: Time and Work
by Damber Pradhan - Wednesday, 27 January 2016, 11:18 PM
  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