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Time and Workby 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 busineschools (India and Abroad). And who would write about verbal? No clue. The admissionprocess, the happenings at business schools, interviews and group discussions used to exciteme more than anything else in CAT arena. But as I moved closer to digging more informationabout business schools, I realized that Indian business schools do not have a very transparenadmissions process. As far as learning goes, I started feeling the stagnation. I was not seeingmuch growth in that area and I did not want to move to the GMAT arena when I had yet notexplored the Indian exams to their full potential. Back then, my love for language was not atits peak but I thought verbal was where I could be. I do not know when I decided to step intoCAT Verbal Forum but I just took the step. As I started working in the CAT Verbal Forum, Istarted connecting with students on both personal and professional level. Today, if I want tocount 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 andInternational 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 strongestsupport. So far you have seen student contributions in the form of CAT articles, you have seen contributions in our CBT Club , and you havseen 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 biggeexposure. TG has really grinded him in solving loads of questions and he has been continuously working on the article from past many day

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

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 problemby 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 c an 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)

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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 joi

him. He also invites Walcott and Fabregas who can dig only 1/5th as fast as he can (Ineffic ient 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 tak

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 nextthree 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 capac ity to do the work is twice that of X, joined. On the third day another man whose capac ity 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. S

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 a

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 peopl

doing the work together in the ratio of total work done by each of them. Again I will explain this with the help o

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 reservo

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 = 18

(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 L2nd 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 47 th minute B is opened and it fills 6 litres.

Hence the reservoir will be full in 47 minutes.

Problem 10: There is an empty reservoir whose capacity is 30 litres. There is an inlet pipe which fills at 5 L/min and

there is an outlet pipe which empties at 4 L/min. Both the pipes function alternately for 1 minute. Assuming that the inle

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 tw

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 3 rd 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.

Rep

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

This article is rea lly very helpful for preparing Time and W ork topic .

Hope to get few more such topics from the author in future.

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Re: Time and Workby sanjeeb panda - Thursday, 9 July 2009, 04:47 PM

Great article.Thanks a lot.

If u have mo re number of questions pls post.

Regards

Sanjeeb

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Re: Time and Workby vishnu m adhavan - Thursday, 9 July 2009, 05:41 PM

Thankuuu soo much Sindhoor.Really nice article

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 MaamRgrdsVishnu

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Re: Time and Workby shivam mehra - Friday, 10 July 2009, 11:15 AM

nice articlethank u so m uch

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

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Re: Time and Workby 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.

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http://totalgadha.com/mod/forum/post.php?reply=55847

http://totalgadha.com/mod/forum/discuss.php?d=5551#55844

























Vishnu, I am happy you liked it ... hoping to see your article someday on TG

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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 encounte

during your preparation.

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Re: Time and Workby Software Engineer - Friday, 10 July 2009, 12:54 PM

Great Effort! Nice Article!

Thanks- SE

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Re: Time and Workby the killer - Friday, 10 July 2009, 03:47 PM

Awsome article Sir!!

Thanks a ton..Hope to get some more articles from you.

Regards,Killer

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Re: Time and Workby 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 ho urs.

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Re: Time and Workby 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 aperson tak es a break while working...

Thanks a ton..

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Re: Time and Workby 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 Workby ayush roy - Saturday, 11 July 2009, 12:38 AM

grt article dude,fe elin so confident nw. just repla ce 180/60 wid 180/30 in p rb 9,just a printin m ista ke .TG sir,expe ctin some challeng ing prbs frm u in this topic.

thanksayush

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Re: Time and Workby akash gupta - Saturday, 11 July 2009, 01:28 AM

too good boss..very helpful

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Re: Time and Workby amit khe terpal - Saturday, 11 July 2009, 10:10 AM

nice work bro..can u give us article on tsd,percentages,prof it 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 morethan my coaching institute.A t the same time iam sad today i got backlog in my 6thsem engineering exams my entire planning is nowshatered.iam not able to understand wat i should do..

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Re: Time and Workby Punee t Aggarwal - Saturday, 11 July 2009, 07:30 PM

after this artice I am feeling lot more confident with time and work.....thanks a lot

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Re: Time and Workby Tuhin Bane rjee - 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

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Re: Time and Workby Parag Paratkar - Saturday, 11 July 2009, 11:38 PM

Hi Sindhoor,

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

-Parag

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Re: Time and Workby joydeep sa rkar - 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 thelast worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in two-third of the time. Howmany workers were there in the group?

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Re: Time and Work

by harshhal bandeka r - 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 wh

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 ...

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Re: Time and Workby 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 findA+B+C's 1 day work). So it is enough to tak e W as the LCM of 75 and 15 which is 75.

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

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Re: joydeepby Kulvir Singh - Monday, 13 July 2009, 12:52 PM

Is the answer three??

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Re: Time and Workby Sindhoor Grandhi - Monday, 13 July 2009, 12:53 PM

Guyz,

Try this problem. Its a good one ..

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Re: Time and Workby 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

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Re: Time and Work

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

@ Sindhoor..Nice a rticle...Which problem you are talking about..??

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Re: Time and Workby Amar Kr Dubedy - Tuesday, 14 July 2009, 03:48 PM

Ans is 6 ??

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Re: Time and Workby joydeep sa rkar - Tuesday, 14 July 2009, 10:43 PM

the answer is 3...

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Re: Time and Workby Vickram Asokan - Wednesday, 15 July 2009, 10:51 AM

Great article...Kudos... Post more challenging problems on the topic..

Thanks,-VIckram.

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Time and Workby Shyam Manawat - Wednesday, 15 July 2009, 05:08 PM









































very nice artical.

i learned a lot. i try to use it in ea ch prob.

thanx

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Re: Time and Workby 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 Workby Sindhoor Grandhi - Wednesday, 15 July 2009, 05:47 PM

Thanks Shyam

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Re: Time and Workby joydeep sa rkar - Wednesday, 15 July 2009, 06:34 PM

Two friends decide to work toge ther and comple te the construction of the fo ur walls o f a room which is in the shape of a square.however,as b fe

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 hadworked together.after this a left and b ,working alone comp leted the cons truction o f the se cond wall and took "(25/16)t" hours more than whatthey would ha ve taken if they had worked together.Finally,both o f them worked together and completed the rema ining two walls.the constructioof the fo ur walls was com pleted in 121 days.

in how many days can b a lone com plete the cons truction of the four walls?

if a total o f 3600 is paid fo r the entire work,what is the share of a ???

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Re: Time and Workby Kulvir Singh - Thursday, 16 July 2009, 12:12 AM

A can make 4 walls in 9 days...

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Re: Time and Workby jyoti ve rma - Friday, 17 July 2009, 12:12 AM

hi

Thanks for the post .

Nice fundas!!

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Re: Time and Workby antriksh a garwal - 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 Workby kumar swambhu - Sunday, 19 July 2009, 10:16 AM

this article have s ome really tricky questions

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Re: Time and Workby 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)tandl+m+n = 121*24 (converting days to hrs)

3 equations n 3 unknowns...solve..enjoy..

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Re: Time and Workby Hema nt 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 i

8 days. If they earned a total of Rs. 5550, then what is the share of Z?Plea se 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. The refore share of Z will be 5550*(12/37) = 1800.

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Re: Time and Workby cc6886 cc - Tuesday, 28 July 2009, 11:39 AM

hi Sindhoor,

wont the ans be true for all mu ltiples of 3 (regarding the no o f workers problem)... i think 6,9 would a lso be right...please correct if am wrong.

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Re: Time and Workby Umang Mathur - Wednesday, 29 July 2009, 04:35 PM

The solution to last problem seems problem spe cific. Had the total man-hours required to complete the work were not 50 but som e creepy

number, then directly multiplying by a number, as in this case by 20, would not be eas ily possible, rather, we would have then

used, hit and trial approach.

Please Correct me if I am wrong.

RegardsUmang

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Re: Time and Workby 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 unde rstand.

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

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Re: Time and Workby Ajaykuma r Kamne - Thursday, 30 July 2009, 10:21 AM

hey tarun,

I had a do ubt in ur solution for the que stion 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 = tm-n = 25t/16and l+m+2n = 121*24 (not l+m+n = 121*24 , 2n be cause they build two walls together.)

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



























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Re: Time and Workby Ajaykuma r Kamne - Thursday, 30 July 2009, 10:49 AM

solution for joydeep's first question,

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

no o f persons working first day = nno of persons working second day = n-1no o f persons working third day = n-2hence 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)*nusing sum of arithmetic progressions and solving this

1/2[2*(a)+(N-1)(d)] = 2N/31/2[2*(1)+(n-1)(1)] = 2n/31/2[n+1] = 2n/3n+1 = 4n/3hence n = 3

and no, n cannot be any multiple of 3 as can be seen here,let x be 1,2,3..... anythingthen our equation would become,xn + xn-1 + xn-2 +.....+1 = (2/3)*xn a nd so lving similarly1/2[2*(a)+(N-1)(d)] = 2N/3, here N = xn1/2[2*(1)+(xn-1)(1)] = 2(xn)/31/2[xn+1] = 2xn/3

xn+1 = 4xn/3xn = 3.n = 3/x (not an integer)Hence n can only take value 3

other ways of s olving this problem are welcome...

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Re: Time and Workby brijesh jadav - Monday, 3 August 2009, 12:18 PM

Great work and an equally great method... thnk u

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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 PRO Bs ON IT.

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Re: Time and Workby harsh Rana - Friday, 7 August 2009, 12:10 AM

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Re: Time and Workby 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

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Re: Time and Workby punit badal - Wednesday, 12 August 2009, 03:16 PM

Hi,

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

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Re: Time and Workby Nikhil Linga la - Thursday, 13 August 2009, 10:00 PM

That was a wesome!! Explained beautifully!!

Thanks so much for the post Sindhoor.

Nikhil

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Re: Time and Workby PAVAN C - Saturday, 15 August 2009, 08:14 PM

Thank you very much for this article.

Regard,pavan

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Re: Time and Workby 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

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Re: Time and Workby 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 onlyis there a better way to so lve???

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Re: Time and Workby 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 abhishek

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Re: Time and Workby Ravi Babu Gudipudi - Friday, 21 August 2009, 03:16 P M

Hi TG,

Thank you, this artical is really good ...

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Re: Time and Workby 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??

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Re: Time and Workby 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-1/45so a's share-(5/9)*3600=2000

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Re: ajaykumar kamneby mitesh anand - Monday, 31 August 2009, 01:22 AM

frnd...I hop k i I will simp lify ur sol little b it..let work done by each prson on ea ch day=1 unitno. o f prsons working on 1st day=n--workdone ->n unitsno. o f prsons working on 2nd da y=n-1--workdone ->n-1 unitsno. o f 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 3discarding 0,ans wud b 3 men.

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Re: Time and Workby Etti R - Saturday, 5 Septembe r 2009, 01:20 AM

Wonderful! a very good variety....please post some more such problems...thanks a lot!!

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Re: Time and Workby Priyesh T ungare - 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 m e...

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Re: Time and Workby nitin bhat - Saturday, 5 September 2009, 11:01 PM

Hi Priyesh,

Pr oblems that include 2 or mor e people can be solved in the similar f ashion 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 wor ks 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 Appr ox.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 Appr ox. 10 Days(9.61).

I hope you have understood b y now....

Regards,

Nitin Bhat

[email protected]

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Re: Time and Workby Priyesh T ungare - 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???

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Re: Time and Workby nitin bhat - Sunday, 6 September 2009, 12:49 AM

Priyesh,

3Days-31 Units of work done, nex t 3 days 62 units done, nex t 3 days 93 units done .... so on and so fo rth by the end of 15 days 155 units ofwork will be comp leted... our target is to comple te 150 units of work.... so it'll be little less than 15 days...

Regards,Nitin

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Re: Time and Workby sindhuja morampalli - Friday, 11 September 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 Workby Neetendra Mishra - Sunday, 13 September 2009, 08:51 PM

gud work...

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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?????

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Re: Time and Workby 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.

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Re: Time and Workby devesh b hattacharya - Friday, 25 September 2009, 07:06 PM

I tried the a pproach its wonde rful.

i tried a few more questions of different variety and placing them here

Q1>

if 20 me n or 24 wome n or 40 boys can do a work in 12 da ys working for 8 hours a day, How many men working with 6 wome n and 2 boys tak eto 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 hou rs.now every group here takes 96 man hours, so,first group o f me n will do 480/96 = 5 units o f work per hour.Same is true for group of women and boys.

each man will do 5/20 unit work pe r hour.each Women do 5/24 unit work per hour,each bo y will do 5 /40 unit per hour.

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

now equatelet no. of men working on new task be = xno. of women working are 6no. o f boys working = 2

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

it gives x = 122which is the no o f men required.

enjoy

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Re: Time and Workby jaya dulan i - Thursday, 1 October 2009, 03:32 PM

Awesome article !!!!

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 o f them constructed two walls together. Moreover, aren't there 4 unkno wns a3 equations? Plz lead me to the correct solution. Thanx..

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Re: Time and Workby arpita bansa l - Saturday, 3 October 2009, 10:27 AM

can someone 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 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 befilled? if the outlert pipe can empty half of the tank in 1 and half hours, the outlet pipe in the middle can em pty 20% of the tank in 1 hr 12 mand outlet pipe at the top can empty 5% of teh tank in 18 mins

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Re: Time and Workby 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 a rticle based on time and distance(Mainly circle problem, A,B, C running and ho w manytimes they meet, kinna........)

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

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Re: Time and Work





















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

Hi

Thank s 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 toprepare as a whole fo r CAT i strongly recomm end you to loo k snapwiz .Take the tests there and compare your percentile score with respe ctiveto each subject. Now a days there is promotional offer going on.i registered through promotional code SW100CATyou can als o try this

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Re: Time and Workby Prudhvi G - Thursday, 8 October 2009, 04:38 PM

Q1> by DeveshIf 20 m en o r 24 women or 40 bo ys can do a work in 12 da ys working for 8 hours a day, How many men working with 6 women and 2 boys taketo 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-HoursAs a group of 20 Men or 24 Women or 40 Boys can do the work in same time20 M = 24 W = 40 B

5 M = 6 W = 10 B (please do not b lame me for gender b ias - ))

Work = 12 x 8 x 20 man-day-hoursNew work = 4 x previous work = 4 x (12 x 8 x 20 ) M-D-HLet 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~Ra j

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Re: Time and Workby sushil krishna - Saturday, 10 October 2009, 03:09 AM

thanx

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Re: Time and Workby manish majumder - Monday, 12 October 2009, 07:07 PM

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

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Re: Time and Workby VENU REDDY - Wednesday, 21 October 2009, 11:24 AM

Time and work articles is really good. Tha nk you very much for posting the a rticle here

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Re: Time and Workby Pankaj Kumar - Thursday, 29 October 2009, 01:02 PM

great n summarized piece on Time a nd Work, TG can you please help us on logarithms topic too.

Thanks!!

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Re: Time and Workby 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 d11 litres are filled into d reservior after dt last 2 steps plz make me understand n problem 3 too!

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Time and Work e bookby prateek ba nsal - 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

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Re: Time and Work e bookby 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 e ff% = 100/5

B does work in 15 da ys so B e ff% = 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 e ff% = 100/15=20/3

A works for 6 days

so work comp leted 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

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

Hello Sir...

Many many thanks to u............In Qua nt,Time and Wo rk was the only section where I have solved any ques tion correctly..........But after goingthrough ur solving skills.........I can solve TnW questions ............Thank s a lot for this great tutorial..........

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Re: Time and Workby 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 lo t guys

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Re: Time and Workby nidhi soni - Sunday, 29 November 2009, 05:27 PM

thnx sindhoo r awesome artical

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Re: Time and Workby 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 atthe beginning?

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

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Re: Time and Workby 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

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Re: Time and Workby 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)*12or, 8x = 12*110-12xor, 4x=12*110or x= 330.

Now plz e xplain!!!

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

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Re: Time and Workby miti chakrabo rty - 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

therefo re, 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...

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Re: Time and Workby miti chakrabo rty - Tuesday, 8 June 2010, 02:56 PM

abhisek,

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

o for the 1st day

10 fo r 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????

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Re: Time and Workby Gul Gul - Tuesday, 8 June 2010, 08:53 PM

Yup Miti, u r correct

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Re: Time and Workby umang shastri - Thursday, 2 September 2010, 03:14 PM

prefect

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Re: Time and Workby 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 hrssecond frnd can comp lete wrk in= X+25t/16,

We also knw that,1/X=1/(X+t)+1/(X+25t/16)from this we get,4X=5tNow use ,(X+t)+(X+25t/16)+2X= 121*24 hrsand calculate the value of X and t.

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Re: Time and Workby Mohit Sharma - Thursday, 5 April 2012, 10:27 PM

Hi Kama l 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 toreduce the time needed by each to make a question by two minutes, then in x minutes Mini would make 2y questions more than Vinay. Howmany questions does Mini make 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 bd) 1/4[2(x-y)-sqrt(2x^2-4y^2)]e) None of these

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Re: Time and Workby Mohit Sharma - Wednesday, 18 April 2012, 06:52 PM

hi Kama l Sir,Please help me with the abo ve question.

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Re: Time and Workby 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 andWalcott.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 so lution provided here the a nswer 100/58 days is absurd be cause that's approx. 1.72 which is greater than 1 day which can't be thecase 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 lesstime.

Plea se check the solution and correct me if i'm wrong.

Thanks.

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Re: Time and Workby kirti vardhan - Sunday, 29 July 2012, 04:39 PM

my first post on TG:

There is a nother concept that can be used to solve time work problem s and that is the FRACTION RULE. I will post a question here.i will give yothe 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 in10 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 begreater 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 m en required = 25*(20/10)*(8/10)= 40 men(answer)

hope this helps u to crack questions faster.

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Re: Time and Workby 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.Show parent | Rep

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

HI Hemant,

Z alone "can do" work in 24 days. But he worked o nly 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 payme nt too 1/3rd only.

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Re: Time and Workby samee r 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 Workby 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

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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..

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Re: Time and Workby jyotsna chauhan - Monday, 22 October 2012, 09:00 PM

hello Sindhoor,Please s olve this question for me . Thank you.

Four pipes can fill a reservoir in 15, 20,30 and 60 hours respectively. The firstone was opened at 6 AM, second at 7AM, third a t 8 AM and the fourth at 9AM. When will the reservoir be filled ?

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Re: Time and Workby 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 take3 hours to fill (30/(4+3+2+1)=3hours) ,

so it will be filled com pletely at 12.00

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