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

SubscribeAptitude22 Comments

IAS Mock Interviews
  1. Prologue
  2. Case: three men start the work simultaneously.
  3. Case: Three Men Start Working One After Another
  4. Case: Share in Daily Wage
  5. Case: Share in money after work finished?
  6. Case: Time equations: set of two people working
  7. Case: Time Ratios are given

Prologue

Speed Time work questions 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 A starts the work and continues for 2 days, then B joins and then C joins ….etc.etc. how much time will it take?

  • Sometimes, Instead of character names, they’ll give your three pipes. Pipe A can fill the tank in X minutes, Pipe B can do in ….But the approach remains the same. (if pipe is emptying then 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 and Champaklal 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?

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

AiyyarBhideChampakTogether
Speed
Time101215
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=2×5

12=22×3

15=3×5

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

LCM=22×31×51=60

  • So LCM (10,12,15)=60. This is the total distance covered, and in this case it means total work done. 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 will remain one and same 60.
AiyyarBhideChampakTogether
Speed
Time101215
Distance60606060

Not only empty box is of speed.

Simply write the number required to get 60 by multiplication.

Example Aiyyer’s time is 10 days. So to get 60 from ten, you’ve to multiply 10 with 6.

(Alternatively) for Aiyyer’s 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 Aiyyar’s speed box.

Similarly for Bhide and Champak you’ll get 5 and 4 respectively.

AiyyarBhideChampakTogether
Speed6546+5+4=15
Time101215
Distance60606060

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

Speed  x time = distance

15 x time = 60

Time = 60/15= 4 days.

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

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 and Champaklal can do it in 15 days. Aiyyar starts painting the society and Bhide joins him after 2 days. 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

CharactersWork
AiyyarBhideChampakAiyyar starts
Speed654  6
Time101215x2
Distance606060=12

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

So in the last column, fill up Aiyyar’s speed and time accordingly.

Speed x time = distance

6 x 2 =12 ; because Aiyyar’s 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 one day. (and then Champak joins)

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

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

CharactersWork
AiyyarBhideChampakAiyyar startsBhide Joins
Speed65466+5=11
x Time101215x2x 1
=Distance60606012=11

Again

Speed x time = distance

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

CharactersWork Progress report
AiyyarBhideChampakAiyyarstartsBhideJoinsChampakJoins
Speed65466+5=116+5+4=15
xTime10121521??
Distance606060601137 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 they’ve asked you to find total number of days required to finish the paint work. So total time is right from the day one when Aiyyar started.

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 the work was finished by Champak in 2 days. If they get Rs.1500 for the whole work. Find the daily wages of Bhide and Champak.

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

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

AbdulBhide
Speed
Time1015
distance15001500

Apply STD formula and find out speed value of each column

AB
Speed150100
xTime1015
=distance15001500

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

ABA+B
Speed150100150+100=250
Time10155
distance15001500250 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.

ABA+BC
Speed150100250
Time101552
distance150015001250250

Run STD formula on C’s column and find his speed

ABA+BC
Speed150100250125
Time101552
distance150015001250250

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 finished?

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

Total road construction is 3200 kms this time.

AB
Speed
Time68
distance32003200

Run STD formula to find speeds

AB
Speed3200/6400
Time68
distance32003200

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

We don’t know the speed of C, assume it is “c” but construct his column and fill remaining data.

ABCA+B+C
Speed3200/6400c(3200/6)+400+c
Time68??3
distance320032003200

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.

Speed x time = distance

(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 long would 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 “SPEED” boxes only and now in the Time boxes.

Now fill up the table.

A+BB+CC+A
SPEED
TIME121520
DISTANCE

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

A+BB+CC+A
SPEED543
TIME121520
DISTANCE606060

Assume that these three entities work together

A+BB+CC+A(A+B)+(B+C)+(C+A)
SPEED5435+4+3=12
TIME121520??
DISTANCE60606060

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

Speed x time = distance

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, is not asked in the question, but I’ve given it only for explanation]

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

A+BB+CC+AA+B+C
SPEED5436
TIME12152010
DISTANCE60606060

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+BB+CC+AA+B+C(A+B+C)-(A+B)=C
SPEED54366-5=1
TIME12152010??
DISTANCE6060606060

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

STD formula,

1 x Time = 60

Hence it’ll take him 60 days.

A+BB+CC+AA+B+C(A+B+C)-(A+B)=C
SPEED54366-5=1
TIME1215201060
DISTANCE6060606060

Do similar procedure for B and A.

A+BB+CC+AA+B+CCBA
SPEED54366-5=16-3=36-4=2
TIME12152010602030
DISTANCE60606060606060

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.

ABCA+BB+CC+A
Speed231543
Time302060121520
Dist606060606060

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. They together finish the work in one day. Find the time taken by each of them to finish the work.

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

A’s time = 6x

B’s time = 3x

C’s Time = 2x

Run the STD table, fill the data

ABCA+B+C
Speed1236
Time6x3x2x1 day
Distance6x6x6x6x

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

Speed x time = distance

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)

ABCA+B+C
Speed1236
Time6321 day
Distance6666

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 to see entire list of all articles published so far!

Mrunal recommends

  1. (free) NCERT, NIOS, TN-Books 4 History,Geo,Sci
  2. Indian Polity M.Laxmikanth (Hindi | English)
  3. Spectrum: Modern History (Hindi | English)
  4. Maths: Quantam CAT Sarvesh Kumar
  5. Objective General English SP Bakshi
  6. Word Power made Easy -Norman Lowe
  7. Topic wise Solved Paperset by Disha

22 Comments on “[Speed Time Work] Three men can finish a work in x days, share in wages & other special cases”

  1. Thanx fr the practice questions mrunal sir !!!!!!! Please give sum guidance on preparation of science and tech. for GS (prelims) !!!!!

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

  3. kindly 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 twelve days
    how many more men are to be added to complete the remaining work in 2 days?

    thanks.

    1. You didn’t take into account the work done by existing group of people(16 men and women) for those two last days. Subtract their share of work done in those two days and calculate men required for completing the work.

  4. Mrunal bhai..kindly tell us..what if 2 persons work alternatively or evry 3rd day and that type eof questions…
    Thank u

  5. Case 3: (short way out)
    assume total time taken = x ;
    then accordingly,
    total work(distance)= 60;
    a’s work = 6*x;
    b’s work = 5*(x-2);
    c’s 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 guys join the party.

  6. Mrunal Sir, plz tell me how to solve this ques with your method or anybody who’ve mastered this method:
    A can do piece of work in 6 days while B can do it in 5 days. If the total amount to be given for this work is Rs.660, what’ll be the share of B if both do the work together?
    Ans: Rs. 360

    1. No need to post this comment. I’ve solved it :D
      Thank you Mrunal Sir, You’r STD method is awesome :D

      1. how u have solved with STD method ??

  7. good…to give such a great explanation

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

  9. thnx #mrunal sir………..it is really helpful

  10. 4men and 6 women get 1600 Rs by doing a piece of work in 5 days . 3 men and 7 women get 1740 Rs by doing same piece of work in 6 days. In how many days, 7 men and 6 women can complete the same work getting 3740 rs?

    Can You explain this problem using STD’s?

    1. Dear Sir,

      Please explain Priya’s question if you can. I am also having this doubt.

  11. Thanx mrunal sir…..

  12. can someone please explain me this step…i don’t know how 6 has come here…2(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

  13. Sir, Please help me with this problem. (SSC CGL Tier-I 2014)

    Three men A,B & C working together can do a job in 6 hours less time than A alone, in 1 hour less time than B alone and in half the time needed by C when working alone. Then A and C together can do the job in??
    a) 2/3 hrs
    b) 3/4 hrs
    c) 3/2 hrs
    d) 4/3 hrs

    1. Kindly provide solution for this

      Three men A,B & C working together can do a job in 6 hours less time than A alone, in 1 hour less time than B alone and in half the time needed by C when working alone. Then A and C together can do the job in??
      a) 2/3 hrs
      b) 3/4 hrs
      c) 3/2 hrs
      d) 4/3 hrs

  14. 1.A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :

    Please show how to use ur trick in this problem?

    2.A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do

    this too…

    Thanks

    1. solution 1
      ———————————————-
      A B A+B
      S 4 3 7
      T 15 20 *4
      D 60 60 28
      Remainning work =60-28=32 units remainning work/total work = 32/60 =8/15 ans
      —————————————————

  15. 540 man-days of work can be completed by a certain number of men in some days. If the numbers of people (men) are increased by 27, then the number of day required to complete the same work is decreased by 15. The number of days are required to complete the three times work (than the previous/actual work) by 27 men?

    1)50
    2)60
    3)54
    4)45…………….

    Need answer to the above question sir !!!thank you
    sir ur website is of great use to me !!thank you for making calculatons look simple !!!

  16. A and B together can do a piece of work in 30 days. B and C together can do it in 20 days. A starts the work and works on it for 5 days, then B takes up and works for 15 days. Finally C finishes the work in 18 days. The number of days in which C alone can do

Leave a Reply

Your email address will not be published. Required fields are marked *