[Speed Time Work] Three Men Can Finish a Work in x Days, Share in Wages & Other Special Cases - Mrunal

Aptitude (http://mrunal.org/category/aptitude) / 3 years Ago /18 Comments (http://mrunal.org/2012/11/speed-time-work-three-men-can-finish-work-x-days-share-wages-special-cases.html#comments)

1. Prologue2. Case: three men start the work simultaneously.3. Case: Three Men Start Working One After Another4. Case: Share in Daily Wage5. Case: Share in money after work finished?6. Case: Time equations: set of two people working7. Case: Time Ratios are given

Prologue

Speed Time workquestions routinely appears in almost every aptitude exam

A can complete a piece of work in 10 days, B can do it in 12 days, C can to it in 15 days. Now Astarts the work and continues for 2 days, then B joins and then C joins .etc.etc. how muchtime will it take?

Sometimes, Instead of character names, theyll give your three pipes. Pipe A can fill the tankin X minutes, Pipe B can do in .But the approach remains the same. (if pipe is emptyingthen use minus sign in the speed.)Such questions take very little time. Just LCM, fill in the table, and use STD formula and done.

Case: three men start the work simultaneously.

Aiyyar can paint Gokuldham society in 10 days, Bhide Master can do it in 12 days andChampaklal can do it in 15 days. If all three of them start working simultaneously from day 1,how many days will it take for them to finish the painting work?

[Speed Time Work] Three men can nish a work in x days, share inwages & other special cases

English: SP Bakshi(http://www.flipkart.com/objective-general-

english-2012/p/itmdyuqqgafhtehp?pid=9788183480000&affid=mrunalrugm)

Mrunal (http://mrunal.org/)

It is similar to the pipes and cisterns problem.so make a table

Aiyyar Bhide Champak Together

Speed

Time 10 12 15

Distance

The time for each individual character, is already given in the problem.

Now take the LCM of Time, means that factorize number into its prime numbers(2,3,5,7,11,13,17,19 etc)

10=25

12=2 3

15=35

Now take each prime number in its highest power and multiply them together.

LCM=2 3 5 =60

So LCM (10,12,15)=60. This is the total distance covered, and in this case it means total workdone. i.e. entire surface area of walls of Gokuldham is 60 square meters.Whether these characters paint the society individually or together, the area of the walls willremain one and same 60.


Speed

Time 10 12 15

Distance 60 60 60 60

2

2 1 1

Not only empty box is of speed.

Simply write the number required to get 60 by multiplication.

Example Aiyyers time is 10 days. So to get 60 from ten, youve to multiply 10 with 6.

(Alternatively) for Aiyyers case

Speed x time = distance

Speed x 10 days = 60 ; because it is already given in the problem that Aiyyar takes 10 days.

Speed = 60/10 = 6.

Write 6, in Aiyyars speed box.

Similarly for Bhide and Champak youll get 5 and 4 respectively.


Speed 6 5 4 6+5+4=15

Time 10 12 15

Distance 60 60 60 60

When these three characters work together, their speed will increase: 6+5+4=15.

Now we have to find out the time required,

Again STD formula


15 x time = 60

Time = 60/15= 4 days.

Final answer: if these three characters work together, they can paint the society in only fourdays.

Case: Three Men Start Working One After Another

Same problem, but with little modification

Aiyyar can paint Gokuldham society in 10 days, Bhide Master can do it in 12 days andChampaklal can do it in 15 days. Aiyyar starts painting the society and Bhide joins him after 2days. Then Both of paint the society together for one day and then Champaklal joins the gang.In this manner, how many total days will be required to finish the paint work?

Part I: Aiyaar starts the work

The table remains seem up to this part

Characters Work

Aiyyar Bhide Champak Aiyyar starts

Speed 6 5 4 6

Time 10 12 15 x2

Distance 60 60 60 =12

It is given that For the first two days, Aiyyar works alone.

So in the last column, fill up Aiyyars speed and time accordingly.


6 x 2 =12 ; because Aiyyars speed is 6 and he works for 2 days.

Meaning, in the first two days Aiyyar has painted 12 square meters of walls.

How much work remains?

Total 60 minus 12 = 48.

Part II: Bhide joins

it is given that, after two days Bhide master joins and together Aiyyar and Bhide work for oneday. (and then Champak joins)

So make a new column in a table, Aiyyar +Bhide

since theyre working together, this bill will increase and we will do addition : 6 + 5 =11

Characters Work

Aiyyar Bhide Champak Aiyyar starts Bhide Joins

Speed 6 5 4 6 6+5=11

x Time 10 12 15 x2 x 1

=Distance 60 60 60 12 =11

Again


11 x 1 =11

Meaning, in one-day Aiyyar and Bhide painted another 11 square meters.

How much work is left??

48 minus 11 =37

Part III : Champaklal joins

Now Champaklal also joins, so combine speed is 6+5+4=15

and remaining work is 37 We have to find out the time

Characters Work Progress report

Aiyyar Bhide Champak Aiyyarstarts BhideJoins ChampakJoins

Speed 6 5 4 6 6+5=11 6+5+4=15

xTime 10 12 15 2 1 ??

Distance 60 60 60 60 11 37 remains

Again STD

Speed x Time =distance

15 x Time = 37

Time = 37/15= approx. 2.5 days

Caution : This 2.5 is not the final answer. Because theyve asked you to find total number ofdays required to finish the paint work. So total time is right from the day one when Aiyyarstarted.

2+1+2.5=5.5

Final Answer: The work will be finished in 5.5 days.

Case: Share in Daily Wage

Abdul can do a piece of work in 10 days; Bhide in 15 days. They work for 5 days. The rest of thework was finished by Champak in 2 days. If they get Rs.1500 for the whole work. Find the dailywages of Bhide and Champak.

They got Rs.1500 for the whole work, meaning the work is worth Rs.1500 so take it as ourdistance

Repharse: Abdul can do road-construction of 1500 kms in 10 days!.. and so on

Abdul Bhide

Speed

Time 10 15

distance 1500 1500

Apply STD formula and find out speed value of each column

A B

Speed 150 100

xTime 10 15

=distance 1500 1500

Given: they (A and B) worked for five days

A B A+B

Speed 150 100 150+100=250

Time 10 15 5

distance 1500 1500 250 x 5=1250

Combined speed of A+B=250 so in two days they constructed road of 1250 kms.

Remaining work = 1500 minus 1250 = 250kms

This was done by C alone, in two days.

A B A+B C

Speed 150 100 250

Time 10 15 5 2

distance 1500 1500 1250 250

Run STD formula on Cs column and find his speed

A B A+B C

Speed 150 100 250 125

Time 10 15 5 2

distance 1500 1500 1250 250

Their daily wage depends on how much work can they do per day?

Which is actually their speed. E.g. B can construct 100 km roads per day.

So daily wage of B=Rs.100

And daily wage of C=Rs.125

Total daily wage of B and C=100+125=225

Case: Share in money after work nished?

Q. Abdul alone can do a piece of work in 6 days and Bhide alone in 8 days. They undertook to doit for Rs.3200. With the help of Champak, they completed the work in 3 days. How much is to bepaid to Champak?

Total road construction is 3200 kms this time.

A B

Speed

Time 6 8

distance 3200 3200

Run STD formula to find speeds

A B

Speed 3200/6 400

Time 6 8

distance 3200 3200

Given: With the help of C, they completed the work in 3 days.

We dont know the speed of C, assume it is c but construct his column and fill remaining data.

A B C A+B+C

Speed 3200/6 400 c (3200/6)+400+c

Time 6 8 ?? 3

distance 3200 3200 3200

Run STD formula on third column

[ (3200/6)+400+c ] x 3 = 3200

Solve this equation you get c=400/3

Meaning speed of c=400/3

He works for 3 days.


(400/3) x 3 =distance

400= distance

Meaning C covered 400kms

Which means he was paid Rs.400

Case: Time equations: set of two people working

Q. A & B can do a piece of work in 12 days , B and C in 15 , C & A in 20 days. How longwould each take separately to do the same work?

In the STD table, when people come and go, we can do addition and subtraction in the SPEEDboxes only and now in the Time boxes.

Now fill up the table.

A+B B+C C+A

SPEED

TIME 12 15 20

DISTANCE

TAKE THE LCM (12, 15, 20) =60. Based on that we can find individual speeds using STD formula.

A+B B+C C+A

SPEED 5 4 3

TIME 12 15 20

DISTANCE 60 60 60

Assume that these three entities work together

A+B B+C C+A (A+B)+(B+C)+(C+A)

SPEED 5 4 3 5+4+3=12

TIME 12 15 20 ??

DISTANCE 60 60 60 60

Speed of A+B+C together can be derived using

(A+B)+(B+C)+(C+A)

= 2(A+B+C)=5+4+3=12

Hence speed of A+B+C together =12/2=6

Now STD formula


6 x time = 60

Time = 10

Meaning if A+B+C work together, they can finish work in 10 days. [Although Time of A+B+C, isnot asked in the question, but Ive given it only for explanation]

Now back to the question, weve to find individual time. So far our table looks like this-

A+B B+C C+A A+B+C

SPEED 5 4 3 6

TIME 12 15 20 10

DISTANCE 60 60 60 60

Now you can solve it three unknown equation.

Because this is speed, we can do addition, subtraction and solve it as three unknown equations

Speed of A+B+C=6

Speed of A+B=5

Hence speed of C= 6 (A+B)= 6-5=1

A+B B+C C+A A+B+C (A+B+C)-(A+B)=C

SPEED 5 4 3 6 6-5=1

TIME 12 15 20 10 ??

DISTANCE 60 60 60 60 60

Speed of C is 1 and he has to cover 60 kilometers alone,

STD formula,

1 x Time = 60

Hence itll take him 60 days.

A+B B+C C+A A+B+C (A+B+C)-(A+B)=C

SPEED 5 4 3 6 6-5=1

TIME 12 15 20 10 60

DISTANCE 60 60 60 60 60

Do similar procedure for B and A.

A+B B+C C+A A+B+C C B A

SPEED 5 4 3 6 6-5=1 6-3=3 6-4=2

TIME 12 15 20 10 60 20 30

DISTANCE 60 60 60 60 60 60 60

Final answer, time taken by A,B,C if they work individually= 30,20,60

Run a cross verification to see the answer is correct. Plug the answer values.

A B C A+B B+C C+A

Speed 2 3 1 5 4 3

Time 30 20 60 12 15 20

Dist 60 60 60 60 60 60

Yes it satisfies the statements given in the Question.

Case: Time Ratios are given

Q. A takes twice as much time as B and thrice as much as C to finish a piece of work. Theytogether finish the work in one day. Find the time taken by each of them to finish thework.

A takes twice as much time as B,

meaning if B takes 1 day, A takes 2 days

So the ratio of time is A:B=2:1

Similarly A:C=3:1

We can write the same thing as

B:A=1:2

A:C=3:1

If we want the three terms ratio, we want mid term (A) to be same in both equation.

In the first eq. A is 2 and in second eq. A is 3. LCM (2,3)=6

Multiply something in both equations so that we get 6 in both equation.

Meaning, Multiply first eq with (2) and second equation with (3)

B:A=3:6

A:C=6:2

Now we can make a three terms ratio

B:A:C=3:6:2

Keep in mind, this is ratio and not absolute number

So we fill Time boxes as

As time = 6x

Bs time = 3x

Cs Time = 2x

Run the STD table, fill the data

A B C A+B+C

Speed 1 2 3 6

Time 6x 3x 2x 1 day

Distance 6x 6x 6x 6x

LCM of (6x,3x,2x)= 6x

From the STD fomula, we can get the individual speeds of A,B,C,= 1,2,3

Together their speed A+B+C=1+2+3=6

For the last column


6 multiplied with 1 =6x

Hence x= 1

Put the value of x=1 in the table and you get individual time

A will take 6 days individually, B will take 3 days and C will take 2 days.

Cross verification (plug the answers we got)

A B C A+B+C

Speed 1 2 3 6

Time 6 3 2 1 day

Distance 6 6 6 6

From the table,

A takes twice as much time as B and thrice as much as C to finish a piece of work

Yes it satisfies the statement given in the question itself.

Visit Mrunal.org/Aptitude (http://Mrunal.org/Aptitude) to see entire list of all articles publishedso far!

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R E P L Y ( / 2 0 1 2 / 1 1 / S P E E D - T I M E - W O R K - T H R E E - M E N - C A N - F I N I S H - W O R K - X - D A Y S - S H A R E - W A G E S -S P E C I A L - C A S E S . H T M L ? R E P L Y T O C O M = 2 0 5 0 7 0 # R E S P O N D )

aditya swaroopThanx fr the practice questions mrunal sir !!!!!!! Please give sum guidanceon preparation of science and tech. for GS (prelims) !!!!!


aditya swaroopPlease guide as to on which portions of technology one must focus ?????Questions frm biology and physics came in 2013 pre. but they were lessthan the technology questions !! Pls guide


sunny kumarkindly help with below question-my answer- 48.actual answer-24

twenty four men can complete a work in 16 days.thirty two women can complete the same work in 24 days.sixteen men & sixteen women started working and worked for twelvedayshow many more men are to be added to complete the remaining work in2 days?

thanks.

R E P L Y ( / 2 0 1 2 / 1 1 / S P E E D - T I M E - W O R K - T H R E E - M E N - C A N - F I N I S H - W O R K - X - D A Y S - S H A R E -W A G E S - S P E C I A L - C A S E S . H T M L ? R E P L Y T O C O M = 2 3 3 7 1 3 # R E S P O N D )

Ghufran AlamYou didnt take into account the work done by existing group ofpeople(16 men and women) for those two last days. Subtract theirshare of work done in those two days and calculate men requiredfor completing the work.


AvinashMrunal bhai..kindly tell us..what if 2 persons work alternatively or evry3rd day and that type eof questionsThank u


AmitCase 3: (short way out)assume total time taken = x ;then accordingly,total work(distance)= 60;as work = 6*x;bs work = 5*(x-2);cs work = 4*(x-3);all 3 guys working,should add up to 60; thus, x = 82/15;

It removes the redundancy of solving remainin work when other guysjoin the party.


NehaMrunal Sir, plz tell me how to solve this ques with your method oranybody whove mastered this method:A can do piece of work in 6 days while B can do it in 5 days. If the totalamount to be given for this work is Rs.660, whatll be the share of B ifboth do the work together?Ans: Rs. 360


Neha

No need to post this comment. Ive solved it Thank you Mrunal Sir, Your STD method is awesome

R E P L Y ( / 2 0 1 2 / 1 1 / S P E E D - T I M E - W O R K - T H R E E - M E N - C A N - F I N I S H - W O R K - X - D A Y S -S H A R E - W A G E S - S P E C I A L - C A S E S . H T M L ? R E P L Y T O C O M = 2 6 4 1 6 8 # R E S P O N D )

devendrahow u have solved with STD method ??


swathigoodto give such a great explanation


shivangiawesome ,just loved the way u make it easier and understandable.


shubham tomarthnx #mrunal sir..it is really helpful


priya

4men and 6 women get 1600 Rs by doing a piece of work in 5 days . 3men and 7 women get 1740 Rs by doing same piece of work in 6 days. Inhow many days, 7 men and 6 women can complete the same workgetting 3740 rs?

Can You explain this problem using STDs?


SadiqDear Sir,

Please explain Priyas question if you can. I am also having thisdoubt.


vaibhav shuklaThanx mrunal sir..


sancan someone please explain me this stepi dont know how 6 has comehere2(12)=24 right?

Speed of A+B+C together can be derived using

(A+B)+(B+C)+(C+A)

= 2(A+B+C)=5+4+3=12

Hence speed of A+B+C together =12/2=6


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07-Jul: NBCC Building (http://www.nbccindia.com/nbccindia/nroot/njsp/Career.jsp)

01-Jul: NIELIT Spec. (http://www.nielit.gov.in/recruitments.aspx)

30-Jun: Rajendra Agro. (http://www.mangaldhwani.com/pusa/wp-

content/uploads/2014/09/Advt_-01_2015.pdf )

30-Jun: IIT Kanpur (http://www.iitk.ac.in/new/vacancies-in-administrative-and-technical-

cadre )

28-Jun: ONGC Rajbhasha (NET)

(http://ongcindia.ongc.co.in/wps/wcm/connect/ongcindia/home/career/recruitment+notices/recruitment-

of-olo-2015)

25-Jun: Raj. Industrial Development (http://www.riicorecruitment.org/)

25-Jun: HSCC Noida (http://www.hsccltd.com/)

24-Jun: Haryana Gramin Agro (http://www.shgb.co.in/RecruitmentsandPromotions)

24-Jun: Haryana Gramin Law Officer (http://www.shgb.co.in/RecruitmentsandPromotions)

Medics

14-Jul: MP medical officer (http://www.mppsc.nic.in/)

30-Jun: HAL Medical officer (http://www.hal-

india.com/Common/Uploads/Resumes/144_CareerPDF1_Med-advt-AC.pdf)

ParaMedics

Not At the moment

Deskjobs

05-Aug: NBE Assistants (http://natboard.edu.in)

31-Jul: IIIT Allahabad Gr.C (http://www.iiita.ac.in/announcements.php)

20-Jul: NISER Clerks (http://www.niser.ac.in/drupal_new/)



07-Jul: NBCC Building (http://www.nbccindia.com/nbccindia/nroot/njsp/Career.jsp)

01-Jul: NIELIT Deskjobs (http://www.nielit.gov.in/recruitments.aspx)

13-Jun: Bank Note Press (http://www.jobapply.in/bnpdewas/)

30-Jun: Lucknow Law univ. (http://rmlnlu.ac.in/recruitment-notification-process.html)

30-Jun: Rashtriya Sanskrit Sansthan (http://sanskrit.nic.in/advt_22_05_2015.pdf)

25-Jun: Pawan Hans Limited (http://pawanhans.co.in/site/Careern.aspx)

24-Jun: SJVN (PH) (http://sjvn.nic.in/careerdetail.htm?10/jobdetail)

Faculty

31-Jul: IIIT Allahabad (http://www.iiita.ac.in/announcements.php)

20-Jul: Raipur Univ. (http://www.prsu.ac.in:8010/Univ_Req.aspx)

15-Jul: NIT Puducherry (http://www.nitpy.ac.in/assets/teaching.pdf)

16-Jul: RPSC Home Science (http://rpsconline.rajasthan.gov.in/)



12-Jul: GBPUAT (http://www.gbpuat.ac.in/)10-Jul: NITTTR Chandigarh (http://www.nitttrchd.ac.in )

07-Jul: Palampur, Himachal asst. (http://www.ihbt.res.in/recruit/recruitNotice.php)

06-Jul: PEC Chandigarh (http://pec.ac.in/~pecac/new/jobs)

03-Jul: SKHM Government Medical College (http://www.gmcmewat.ac.in)

30-Jun: IIT Roorkee (http://www.iitr.ernet.in/administration/pages/Openings+Faculty.html)

30-Jun: Ambedkar Uni. Delhi (http://aud.ac.in/careerataud)

30-Jun: NEIGRIHMS (http://neigrihms.gov.in)

30-Jun: Lucknow Law (http://rmlnlu.ac.in/recruitment-notification-process.html)

30-Jun: AIIMS Raipur (http://www.aiimsraipur.edu.in/Career.aspx)

28-Jun: Ranchi Agro (http://www.bauranchi.org/application-for-the-post-of-teachers-2/)

22-Jun: DIATPune (http://14.139.111.180/admin.html)

22-Jun: IGIT (http://www.igitsarang.ac.in/careers.php)

22-Jun: Himachal Central Univ. (http://www.cuhimachal.ac.in/job_emp.aspx)

Uniform

19-Jul: Navy Officers (http://www.irfc-nausena.nic.in/hindi/join_indiannavy.htm)

17-Jul: NDA Officers (http://upsconline.nic.in/mainmenu2.php)

15-Jul: Army Dental (23) (http://indianarmy.nic.in)

10-Jul: Army 10+2 (http://joinindianarmy.nic.in/)

30-Jun: BSF Constable (http://bsf.nic.in/en/recruitment.html)

15-Jun: Navy Sailers (SSR) (http://nausena-bharti.nic.in/forthcomingSailor.php)

15-Jun: Daman Diu Constables (http://daman.nic.in/jobs/2015/616-12-05-2015.PDF)

B.Com,CA,HR,MBA

20-Jul: Pawan Hans Audit (http://pawanhans.co.in/site/Careern.aspx)

06-Jul: GBPUAT Accountant (http://www.gbpuat.ac.in/)

01-Jul: NIELIT Accounts (http://www.nielit.gov.in/recruitments.aspx)

25-Jun: MP Electricity Accounts

(https://www.mponline.gov.in/Portal/Services/Recruit_MPKVV/Indore/notification.aspx)

21-Jun: Lucknow Metro Accounts

1. Online Form Part-I stops few days before deadline, so don't wait till last date. Dont forget

reg.id & roll no.Note'em in Google Drive (https://www.google.com/drive/)

2. I usually update vacancies every Monday.Purple link= newly added,Blue= existing.Last

updated Mon. Jun 22, at 9:04PM

(https://www.digialm.com/EForms/html/form2399/index.html)

RESULT /MARKSHEET

SSC 2014 T2

NCLAT

Hotel Management

TENTATIVE NOTIFICATIONS

IAS-IPS-IFoS: 16 May

IES: 7 Feb

SSC CGL: 2 May

SSC 10+2: 6 June

SSC Sub insp: 28 Mar

CAT: Aug 2015

RBI Officer / Assistant: ??

IBPS PO / Clerk / RRB: ??

ACIO 2015: ??

(https://www.facebook.com/Mrunal.org)

(https://twitter.com/mrunal_patel)

(https://plus.google.com/109455346868280536907?

rel=author)

(http://www.youtube.com/user/TheMrunalPatel)

(http://feedburner.google.com/fb/a/mailverify?

uri=CivilServiceExam)HOME (HTTP://MRUNAL.ORG/) ECONOMY (HTTP://MRUNAL.ORG/ECONOMY)

DOWNLOAD (HTTP://MRUNAL.ORG/DOWNLOAD) CONTACT ME (HTTP://MRUNAL.ORG/CONTACT)

The work of Mrunal (http://mrunal.org/) is under the Creative Commons Attribution-Non Commercial-ShareAlike 4.0License (http://creativecommons.org/l icenses/by-nc-sa/4.0/deed.en_US).Permissions beyond the scope of this l icense

may be available at Mrunal.org/contact (http://mrunal.org/contact).

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[Speed Time Work] Three Men Can Finish a Work in x Days, Share in Wages & Other Special Cases - Mrunal

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