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by Sindhoor Grandhi - Thursday, 9 July 2009, 01:59 PM

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?

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 ) 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.

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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.

1

Minute => A is opened => fills 9 L

2

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

3

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

minute A is opened and it fills 9 litres. In the 47

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

Minute => inlet pipe opened => 5l filled

2

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

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.

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 4

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 3

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 20

hour.

Reply

Re: Time and Work

by Rahul Shinde - Thursday, 9 July 2009, 04:42 PM

This article is really very helpful for preparing Tim e and Work topic . Hope to get few m ore such topics from the author in future.

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Re: Time and Work

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

Great article.Thanks a lot.

If u have m ore num ber of questions pls post.

Regards Sanjeeb

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Re: Time and Work

by vishnu m adhavan - Thursday, 9 July 2009, 05:41 PM Thankuuu soo m uch Sindhoor.Really nice article

The concept of taking work as m ulitple units is sim plifying probs to a grt extent.Thankuu

Hope sm eday, we chotta gadhas too will be providing quality stuff like dis to our gadha land.Thnku TG & Dagny Maam Rgrds

Vishnu

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Re: Time and Work

by shivam m ehra - Friday, 10 July 2009, 11:15 AM nice article

thank u so m uch

problem 7 is bit problem atic...4 or 7 hours a day work is carried out not clear

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Re: Time and Work

by Sindhoor Grandhi - Friday, 10 July 2009, 11:28 AM

Thanks Shivam

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

7/5/13

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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 som eday on TG

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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 m ore .. or m ay be you can post any that you encounter during your preparation.

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Re: Time and Work

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

Thanks - SE

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Re: Time and Work

by the killer - Friday, 10 July 2009, 03:47 PM Awsom e article Sir!!

Thanks a ton..

Hope to get som e m ore articles from you. Regards,

Killer

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Re: Time and Work

by Jay Sam pat - Friday, 10 July 2009, 04:44 PM

Thanks A Lot.

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

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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 som e m ore problem s, esp. on pipes n cisterns, and those like the last problem where a person takes a break while working...

Thanks a ton..

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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

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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 m istake. TG sir,expectin som e 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

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Re: Time and Work

by am it 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.A t 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..

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Re: Time and Work

by Puneet Aggarwal - Saturday, 11 July 2009, 07:30 PM

after this artice I am feeling lot m ore confident with tim e and work...thanks a lot

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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 som e good quality questions here specific to Tim e & Work? Regards,

Tuhin

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Re: Time and Work

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

Thanks for the article... !!!!! -Parag

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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?

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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

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Please clarify ...

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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 assum e Work as; rem em ber 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 sam e answer. You need to take a m ental note of what you would be dividing W with while you are solving the problem . Got it? Tell m e frankly if you still have a doubt ..

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Re: joydeep

by Kulvir Singh - Monday, 13 July 2009, 12:52 PM Is the answer three??

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Re: Time and Work

by Sindhoor Grandhi - Monday, 13 July 2009, 12:53 PM

Guyz,

Try this problem . Its a good one ..

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Re: Time and Work

by Gaurav Mittal - Monday, 13 July 2009, 04:00 PM

great work done sindhoor... hope to see som e m ore articles like this from you in future... thanks a lot

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Re: Time and Work

by Kulvir Singh - Tuesday, 14 July 2009, 11:57 AM @ Sindhoor..

Nice article...

Which problem you are talking about..??

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Re: Time and Work

by Am ar Kr Dubedy - Tuesday, 14 July 2009, 03:48 PM Ans is 6 ??

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Re: Time and Work

by joydeep sarkar - Tuesday, 14 July 2009, 10:43 PM the answer is 3...

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Re: Time and Work

by Vickram Asokan - Wednesday, 15 July 2009, 10:51 AM Great article...

Kudos... Post m ore challenging problem s on the topic.. Thanks,

-VIckram .

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Time and Work

very nice artical.

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

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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

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Re: Time and Work

by Sindhoor Grandhi - Wednesday, 15 July 2009, 05:47 PM

Thanks Shyam

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Re: Time and Work

by joydeep sarkar - Wednesday, 15 July 2009, 06:34 PM

Two friends decide to work together and com plete 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 com pleted the construction of one wall and took "t" hours m ore than what they would have taken if they had worked together.after this a left and b,working alone com pleted the construction of the second wall and took "(25/16)t" hours m ore than what they would have taken if they had worked together.Finally,both of them worked together and com pleted the rem aining two walls.the construction of the four walls was com pleted in 121 days.

in how m any days can b alone com plete the construction of the four walls? if a total of 3600 is paid for the entire work,what is the share of a???

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Re: Time and Work

by Kulvir Singh - Thursday, 16 July 2009, 12:12 AM A can m ake 4 walls in 9 days...

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Re: Time and Work

by jyoti verm a - Friday, 17 July 2009, 12:12 AM

hi

Thanks for the post . Nice fundas!!

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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

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Re: Time and Work

by kum ar swam bhu - Sunday, 19 July 2009, 10:16 AM this article have som e really tricky questions

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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..

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Re: Time and Work

by Hem ant 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 m e 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.

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Re: Time and Work

by cc6886 cc - Tuesday, 28 July 2009, 11:39 AM hi Sindhoor,

wont the ans be true for all m ultiples of 3 (regarding the no of workers problem )... i think 6,9 would also be right... please correct if am wrong.

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Re: Time and Work

by Um ang Mathur - Wednesday, 29 July 2009, 04:35 PM

The solution to last problem seem s problem specific. Had the total m an-hours required to com plete the work were not 50 but som e creepy

number, then directly multiplying by a number, as in this case by 20, would

Please Correct m e if I am wrong. Regards

Um ang

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Re: Time and Work

by diptadeep banerjee - Wednesday, 29 July 2009, 10:22 PM

hi Hem ant,

I think we need to consider the ratio of work done rather than the tim e taken in doing the work.. that's what i understand. Can anyone tell m e how to solve joydeep's first question please?

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Re: Time and Work

by Ajaykum ar Kam ne - 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 am ount 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 m e if am wrong.

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Re: Time and Work

by Ajaykum ar Kam ne - 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 arithm etic 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 m ultiple of 3 as can be seen here, let x be 1,2,3... anything

then our equation would becom e,

xn + xn-1 + xn-2 +...+1 = (2/3)*xn and solving sim ilarly 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 welcom e...

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Re: Time and Work

by brijesh jadav - Monday, 3 August 2009, 12:18 PM Great work and an equally great m ethod... thnk u

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Re: Time and Work

by m anish kakati - Tuesday, 4 August 2009, 06:23 PM

I getting the concepts...but som e m ore problem s will strengthen our basics and acum en... PLEASE PROVIDE MORE PROBs ON IT.

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Re: Time and Work

by harsh Rana - Friday, 7 August 2009, 12:10 AM

Wow...Awe-inspiring explanation about Tim e and Work Topic. As usual sam e like other covered topics on this site. I feel am azed whenever i read your topics here and you guys m ake m e addicted of your m arvellous site. This site really educate m e for m y MBA form ulations. Just, a week before got to know about TathaGat and now it'll becom e m y diurnal habbit of surfing on this website. Infact, i already send you a 1600/-cheque for CAT CBT m em bership and num ber system or geom etry e-book. Hope you will respond ASAP.

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Cheers

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Re: Time and Work

7/5/13

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Hi,

I had pre-conceived notion that Tim e and work is tedious.. but this article has m ade it sim pler and lucid.. Thanks

-Hari

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Re: Time and Work

by punit badal - Wednesday, 12 August 2009, 03:16 PM

Hi,

could you put som e probem s which involve persons with different capabilities...

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Re: Time and Work

by Nikhil Lingala - Thursday, 13 August 2009, 10:00 PM That was awesom e!! Explained beautifully!!

Thanks so m uch for the post Sindhoor. Nikhil

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Re: Time and Work

by PAVAN C - Saturday, 15 August 2009, 08:14 PM Thank you very m uch for this article.

Regard, pavan

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Re: Time and Work

by m anish kakati - Wednesday, 19 August 2009, 11:23 AM

Please this for m e:

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

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Re: Time and Work

by kanwarjit chadha - Wednesday, 19 August 2009, 09:14 PM Boss,

ans is 40 m in

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 m ore of ur noble work.have a great day ahead cheers abhishek

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Re: Time and Work

by Ravi Babu Gudipudi - Friday, 21 August 2009, 03:16 PM

Hi TG,

Thank you, this artical is really good ...

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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 m e why u equated these two term s??

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Re: Time and Work

by m itesh anand - Monday, 31 August 2009, 01:07 AM hi everyone,

the ans for joydeep's 2nd prob wud

be--b can com plete in 45*4=180 days(only I think u m ight hav m istaken in writing hrs instead of dayz at sum places) a-1/36,b-1/45

so a's share-(5/9)*3600=2000

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Re: ajaykumar kamne

by m itesh anand - Monday, 31 August 2009, 01:22 AM frnd...I hop ki I will sim plify 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 becom es->

n + n-1 + n-2 + ... +1=(2/3)[n+n+n...upto 'n' tim es] [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 m en.

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Re: Time and Work

by Etti R - Saturday, 5 Septem ber 2009, 01:20 AM

Wonderful! a very good variety....please post som e m ore such problem s...thanks a lot!!

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Re: Time and Work

by Priyesh Tungare - Saturday, 5 Septem ber 2009, 09:44 PM hiii...

can anyone explain m e the problem s where two or m ore people are included and they work on alternate days?? i am not able to solve this kind of problem s.. please help m e...

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Re: Time and Work

by nitin bhat - Saturday, 5 Septem ber 2009, 11:01 PM Hi Priyesh,

7/5/13

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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

[email protected]

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Re: Time and Work

by Priyesh Tungare - Saturday, 5 Septem ber 2009, 11:19 PM hey nitin...

it m ay 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 com plete the work???

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Re: Time and Work

by nitin bhat - Sunday, 6 Septem ber 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 com pleted... our target is to com plete 150 units of work.... so it'll be little less than 15 days...

Regards, Nitin

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Re: Time and Work

by sindhuja m oram palli - Friday, 11 Septem ber 2009, 04:05 PM

really a great work thank u so m uch sir

keep updating these kind of works

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Re: Time and Work

by Neetendra Mishra - Sunday, 13 Septem ber 2009, 08:51 PM gud work...

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Re: Time and Work

by ram krishna roy - Thursday, 17 Septem ber 2009, 03:54 PM for exam ple-3. , how are we getting LCM to be 600?????

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Re: Time and Work

by PAVAN C - Tuesday, 22 Septem ber 2009, 12:31 AM Dear ram krishna 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 Septem ber 2009, 07:06 PM I tried the approach its wonderful.

i tried a few m ore questions of different variety and placing them here Q1>

if 20 m en or 24 wom en or 40 boys can do a work in 12 days working for 8 hours a day, How m any m en working with 6 wom en and 2 boys take to do a job 4 tim es 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 m an hours. now every group here takes 96 m an hours, so,

first group of m en will do 480/96 = 5 units of work per hour. Sam e is true for group of wom en and boys.

each m an will do 5/20 unit work per hour. each Wom en do 5/24 unit work per hour, each boy will do 5/40 unit per hour.

now the new task is 4 tim es bigger i.e 480*4 units. now equate

let no. of m en working on new task be = x no. of wom en 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 m en required. enjoy

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Re: Time and Work

by jaya dulani - Thursday, 1 October 2009, 03:32 PM

Awesom e article !!!!

U've m ade tim e & work probs m uch easier and interesting for m e.. 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 m e to the correct solution. Thanx..

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Re: Time and Work

by arpita bansal - Saturday, 3 October 2009, 10:27 AM

can som eone please help m e in solving this question:

a large tank of height 10m is fitted with an inlet which can fill it in 60 m inutes. the tank has 3 outlet pipes fitted at the heights of 5m , 8m , 9.5m , from the bottom . all the pipes are opened sim ultaneously, with the tank being em pty initially. in how m uch tim e 95% of the tank can be filled? if the outlert pipe can em pty half of the tank in 1 and half hours, the outlet pipe in the m iddle can em pty 20% of the tank in 1 hr 12 m in and outlet pipe at the top can em pty 5% of teh tank in 18 m ins

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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 tim e and distance(Mainly circle problem , A,B, C running and how m any tim es they m eet, kinna...)

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

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7/5/13

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by supriya naidu - Thursday, 8 October 2009, 12:34 PM

Hi

Thanks for the inform ation.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 recom m end you to look snapwiz .Take the tests there and com pare your percentile score with respective to each subject. Now a days there is prom otional offer going on.i registered through prom otional code SW100CAT

you can also try this

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Re: Time and Work

by Prudhvi G - Thursday, 8 October 2009, 04:38 PM Q1> by Devesh

If 20 m en or 24 wom en or 40 boys can do a work in 12 days working for 8 hours a day, How m any m en working with 6 wom en and 2 boys take to do a job 4 tim es larger, if they work 5 hours a day for 12 day?

Alternate solution

As a group of 20 Men or 24 Wom en or 40 Boys can do the work in sam e tim e 20 M = 24 W = 40 B

5 M = 6 W = 10 B (please do not blam e m e for gender bias - )) Work = 12 x 8 x 20 m an-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 m en ~Cheers~

Raj

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Re: Time and Work

by sushil krishna - Saturday, 10 October 2009, 03:09 AM thanx

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Re: Time and Work

by m anish m ajum der - Monday, 12 October 2009, 07:07 PM

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

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Re: Time and Work

by VENU REDDY - Wednesday, 21 October 2009, 11:24 AM

Tim e and work articles is really good. Thank you very m uch for posting the article here

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Re: Time and Work

by Pankaj Kum ar - Thursday, 29 October 2009, 01:02 PM

great n sum m arized piece on Tim e and Work, TG can you please help us on logarithm s topic too. Thanks!!

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Re: Time and Work

by sm riti chhabra - Wednesday, 4 Novem ber 2009, 10:53 AM

hi! ds article s really helpful! plz gve such articles n all im portant topics n CAT! but i ve sm e doubts in problem 9 ve understood upto dt levet dt 11 litres are filled into d reservior after dt last 2 steps plz m ake m e understand n problem 3 too!

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Time and Work e book

by prateek bansal - Tuesday, 10 Novem ber 2009, 02:15 AM tg sir

prateek

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Re: Time and Work e book

by jatin arora - Tuesday, 10 Novem ber 2009, 12:50 PM

Dear Sir ,

the problem s 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 com pleted by A in 6 days = (20/3)*6 = 40% so work to be com pleted by B in 3 days = 60% B eff% = 60/3 = 20%

So B alone can do work in = 100/20

= 5 days answer

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Re: Time and Work

by Sam it Katiyar - Monday, 16 Novem ber 2009, 09:34 PM

Hello Sir...

Many m any thanks to u...In Quant,Tim e 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...

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Re: Time and Work

by Ankit Garg - Tuesday, 24 Novem ber 2009, 11:12 AM

great article ... after reading i realized how sim ple it will be with taking LCM ... thanks a lot guys

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Re: Time and Work

by nidhi soni - Sunday, 29 Novem ber 2009, 05:27 PM

thnx sindhoor awesom e artical

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Re: Time and Work

by abhishek rai - Tuesday, 8 June 2010, 04:31 AM I m ay be an idiot, but please see the following.

A group of m en decided to do a job in 8 days. But since 10 m en dropped everyday, the job got com pleted in 12 days. How m any m en were at the beginning?

I got the answer as 330. Am I correct. I think the answer, given as 165 is wrong..Help!!!

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Re: Time and Work

by Gul Gul - Tuesday, 8 June 2010, 08:58 AM Abhishek,

7/5/13

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The equation would be sth like this: 8x = 12x - 10(1+2+...11)

x= 165

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Re: Time and Work

by abhishek rai - Tuesday, 8 June 2010, 01:49 PM Thnx Gulab...

But accroindgly, 660 m en dropped in 12 days, but only 165 m en 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 m andays required 1320, if 165 is the answer and after after dropping of 110 people, it becom es 540. Som ething fishy!

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Re: Time and Work

by m iti chakraborty - Tuesday, 8 June 2010, 02:29 PM

ajay,

i used sim ple trial nd error m ethod 2 solve dis q... here, t1/t2= 1/(2/3) = 3/2

therefore, w1/w2= 2/3

nw capacity of each person is sam e. Let us assum e 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 tim e saving...

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Re: Time and Work

by m iti chakraborty - Tuesday, 8 June 2010, 02:56 PM

abhisek,

the no. of m en dropped during the process is :-o f:-or the 1st day

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

i.e. in total (10 X11)= 110 m en were dropped according to the q am i right, gulab????

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Re: Time and Work

by Gul Gul - Tuesday, 8 June 2010, 08:53 PM Yup Miti, u r correct

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Re: Time and Work

by um ang shastri - Thursday, 2 Septem ber 2010, 03:14 PM prefect

Re: Time and Work

by Mohit Sharm a - Tuesday, 3 April 2012, 09:58 AM @ joydeep,

Let both the frnd can com plete the wrk in X hrs, then, first frnd can com plete wrk in= X+t hrs second frnd can com plete 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.

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Re: Time and Work

by Mohit Sharm a - Thursday, 5 April 2012, 10:27 PM Hi Kam al Sir,

Please help m e with the question.

Ques: Mini and Vinay are quiz m asters preparing for a quiz. In x m inutes, Mini m akes y questions m ore than Vinay. If it were possible to reduce the tim e needed by each to m ake a question by two m inutes, then in x m inutes Mini would m ake 2y questions m ore than Vinay. How m any questions does Mini m ake in x m inutes?

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

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Re: Time and Work

by Mohit Sharm a - Wednesday, 18 April 2012, 06:52 PM hi Kam al Sir,

Please help m e with the above question.

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Re: Time and Work

by Kirti Sahoo - Wednesday, 6 June 2012, 10:31 AM Hello TG,

I think there's a bit of an anom aly in the solution for Problem 4.

In the solution it's given that Lapm pard and Rooney's 1 day work = 15 units but i think it should be 1 hours work and sam e with Fabregas and Walcott.

So there com bined 1 hours work should be 39 units and thus they can com plete 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 him self takes 5 hours to com plete the work so with the help of 4 other people he should be able to com plete the work in less tim e.

Please check the solution and correct m e if i'm wrong. Thanks.

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Re: Time and Work

by kirti vardhan - Sunday, 29 July 2012, 04:39 PM m y first post on TG:

There is another concept that can be used to solve tim e work problem s and that is the FRACTION RULE. I will post a question here.i will give you the easy m ethod.

25 m en and 20 days to construct a 10 m t wall.how m any m en are required to m ake an 8 m t wall if it is planned that the work be com pleted in 10 days..

FRACTION RULE:

take the value of the quantity that is to be calculated as reference..here 25. then fram e the fractions by the following:

if num ber of days decreases (20 to 10) the num ber m en has to inclrease so the fraction that has to be m ultiplied should be greater than 1 so 20/10.

next for constructin an 8 m t wall lesser num ber of m en are required as com pared to a 10m t wall so the fraction has to be less than 1 i.e. 8/10 so m en required = 25*(20/10)*(8/10)= 40 m en(answer)

hope this helps u to crack questions faster.

7/5/13

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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.

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Re: Time and Work

by Rhythm Goyal - Sunday, 5 August 2012, 10:57 PM

HI Hem ant,

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

Also paym ent does not depend on num ber of days worked for, but on the am ount of work. Thus in 8 days he worked 1/24*8 part of work i.e. 1/3 of work.thus paym ent too 1/3rd only.

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Re: Time and Work

by sam eer sapre - Sunday, 5 August 2012, 11:17 PM thank you sir...!!

gr8 and laudable work. thanks a lot...!!

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Re: Time and Work

by Ashwani Kushwaha - Friday, 24 August 2012, 03:23 PM

cud anyone out here provide m e the link to the Ratio and proportion forum . I can't find it. It would be of great help. thanx

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Re: Time and Work

by anil m osali - Monday, 10 Septem ber 2012, 07:43 AM

u r genius boss. Actually speaking u r total n we are gadhas.. thats our site. help us im prove still m ore with concepts of deeper com plexity..

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Re: Time and Work

by jyotsna chauhan - Monday, 22 October 2012, 09:00 PM hello Sindhoor,

Please solve this question for m e . 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 ?

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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 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 com pletely at 12.00

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