[Aptitude] Time n Work: 4 men and 6 women can complete a work in 8 Days then

MK Pandey Fast track to objective arithmetic

This is merely a subtype of Time n Work problems. and can be solved using our good ol’ STD table Method.

  1. Case 1: Women finish entire job
  2. Case 2: Women to finish remaining job
  3. Case: Child labour

Case 1: Women finish entire job

4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

Suppose 1 man can pour 1 bucketful of water in the tank in 1 minute.
If 6 men work together, they pour 6 buckets in a tank in 1 minute.
In short, you multiply the speed with number of person.

Our usual table

1 Man 1 Woman 4 men & 6 women 3 men & 7 women
Speed m w 4m+6w 3m+7w
Time 8 10
distance

Distance covered in each column is same.
So compare last two columns
Distance = distance
Speed x time = speed x time
(4m+6w)*8=(3m+7w)*10

Solve this equation and you get m=11w
Replace this value of w in last column

1 Man 1 Woman 4 men & 6 women 3 men & 7 women
Speed m w 4m+6w 3(11w)+7w
Time 8 10
distance

3(11w)+7w
=33w+7w
=40w

1 Man 1 Woman 4 men & 6 women 3 men & 7 women
Speed m w 4m+6w 40w
Time 8 10
distance 40w x 10= 400w

So the total work is
Speed x time = distance
40w x 10= 400w

If 10 women work together, they’ve to cover 400w kms. Make a new column, run STD formula

1 Man 1 Woman 4 men & 6 women 3 men & 7 women 10 women
Speed m w 4m+6w 40w 10w
Time 8 10 ??
distance 40w x 10= 400w 400w

10w x time =400w
Time =400w/ 10w=40days.

Answer: If 10 women work together, it’ll take 40 days to finish the job.

Case 2: Women to finish remaining job

12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on the job to complete the remaining work, if it is to be completed in 3 days?

12 Man 15 Woman
Speed 12m 15w
Time 4 4
distance

Distance covered in both column is same so compare them

Speed x time = speed x time
12m x 4= 15w x 4
4m=5w
M=(5/4)w

The question is asking about number of women in the end, so better convert everything in terms of women.
Given:  6 men start working on the job and after working for 2 days, all of them stopped working
Make a new column.

12 Man 15 Woman 6men
Speed 12m 15w 6x (5/4)w
Time 4 4 2
distance 60w 6x (5/4)w x2=15w

As you can see, I’ve applied STD formula in last two columns to find distance simultaneously.
Remaining work=60w minus 15w=45w
Required: we want to finish this work in 3 days.
Asked: How many women should be put on the job to complete the remaining work, if it is to be completed in 3 days?

Make a new column. Suppose we need “F” number of women so speed = f x w = Fw.

12 Man 15 Woman 6men Find women
Speed 12m 15w 6x (5/4)w Fw
Time 4 4 2 3
Distance 60w 15w 45w

Time limit is given to us: complete remaining work in three days. So t=3 for last column.
Run STD on last column
Fw x 3 =45w
F=45w /3w
F=15
Answer :  15 women required.

Important: Remaining work is to be completed in 3 days. So t=3
If they had asked “total work is to be completed in 3 days”, we’ll need to take t=1, because those men already worked for 2 days to only 1 day left to complete the job (2+1=3 days)

Case: Child labour

Twelve children take sixteen days to complete a work which can be completed by eight adults in twelve days. Sixteen adults started working and after three days ten adults left and four children joined them. How many days will they take to complete the remaining work?

12 kids 8 men
Speed 12k 8m
Time 16 12
Distance

Since work done in both columns is same
Speed x time = speed x time
12k x 16= 8m x 12
K=(1/2)m

Concentrate on middle column (8 men) run STD table on it. You get distance = 8m x 12 =96m
So total distance to be covered is 48m

Given: Sixteen adults started working and after three days ….
Means 16 men worked for 3 days.

12 kids 8 men 16 men
Speed 12k 8m 16m
Time 16 12 3
Distance 8m x 12=96m 16m x 3=48m

We’ve run STD on last column and got that 16 men covered 48m kms.
So remaining work is 96m minus 48m=48m

Given: after three days ten adults left and four children joined them
So now men left =16 minus 10 =6 men and 4 kids joins them so speed is 6m+4k
Make a new column

12 kids 8 men 16 men Men & kids
Speed 12k 8m 16m 6m+4k
Time 16 12 3 ??
Distance 96m 48m 48m

Run STD on last column
(6m+4k) x time =48m
But We already calculated that K=(1/2)m
Apply it in above equation{6m+4(1/2)m}  x time =48m
{6m+2m} x time = 48m
8m x time = 48m
Time =48m /8m
Time=6 days.

Lucent General Knowledge Objective English

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अब तक 55 कमेंट्स लिखी गयी

  1. sandeep says:

    beautifully explained, aptitude seems to be very easy by your explainations sir

  2. sandeep says:

    concepts made very easily, aptitude seems to very easy by your explaination sir

  3. dnt u miss me??? says:

    i dnt knw wats ur future plans , but if u stand for election .. whole youth of india will vote for u !!! mrunal long live …

  4. dnt u miss me??? says:

    i dnt knw wats ur future plan , but if u stand for election whole youth of this country will vote for u . mrunal long live

  5. Avinash says:

    Plz solve dis by ur method: Q) A,B,C can do a piece of work in 12,15,20 days respectively..If A is working all the time, B and C are working alternatively,then in how many days work wil be done?

    • Pooja says:

      ans- 120/17

      as per the technique,
      A B C A+(B/2)+(C/2)
      speed A B C A+(B/2)+(C/2)
      Time 12 15 20 ??
      Distance 12A 15B 20C 12A

      12A=15B=20C

      Now, Time= 12A/[A+(B/2)+(C/2)] _____since time= dist./speed

      By solving above equation u’ll get 120/17 ans.

    • sandeep sinha says:

      Whats the answer??

    • sandeep sinha says:

      I am getting 7 days..I may be wrong..I am known to do silly mistakes!!! :)

      • vandy says:

        u r right …………ans is 7 days

  6. Avinash says:

    Plz also solve other models in work,time,wages like A can do 25 percent work,b does 1/6th work……so on

  7. rupesh says:

    THANK U!!!! so much for giving a such wonderful tricks to solve the problem…………………..THANK u sooo much……….

  8. megha says:

    Mr. A finish a worked on 12 days. when Mr. B finished this work on 15 days and Mr. C on 20 days separately. but after 2days A left the work and B left the work before 2days finished the work. How many day worked will be finished?

    Plz solve this question ?

    • mohit kumar says:

      hello Megha!

      A – 12
      B – 15
      C – 20
      in question they say that after 2 days A left

      now we will find how much work they have done in 2 days

      2*( 1/12 + 1/15 + 1/20 ) = 2/5 it means they have completed 2/5 work .now remaining work

      is 1-2/5 = 3/5

      let form here own-word that they (B and C) finish the work in D days .

      D* 1/20 + (D-2)* 1/15 = 3/5
      form here D comes ——————– 44/7 days.

      final answer is 2 + 44/7 = 58/7 days .

      please replay if i am wrong .

      • kallis says:

        Ur right mohit kumar….I solve it in std technique.I got same answer…:-)

  9. Prashant says:

    Please solve
    5 women and 3 men done any work in 10 days. 4 women and 4 men done this work in 3 days. How many days that 10 women take to done this work?

  10. Pankaj Sharma says:

    Mr. A finish a worked on 12 days. when Mr. B finished this work on 15 days and Mr. C on 20 days separately. but after 2days A left the work and B left the work before 2days finished the work. How many day worked will be finished?

    sol : (more simple)

    let they complete the work in x days then,

    x/20+(x-2)/15+2/12=1;

    => 58/7 days (ans)

    x/20= C’s total work
    (x-2)/15= B’s total work
    2/12 = A’s total work
    (you can do such questions with approach)

  11. Pankaj Sharma says:

    Mr. A finish a worked on 12 days. when Mr. B finished this work on 15 days and Mr. C on 20 days separately. but after 2days A left the work and B left the work before 2days finished the work. How many day worked will be finished?

    sol : (more simple)

    let they complete the work in x days then,

    x/20+(x-2)/15+2/12=1;

    => 58/7 days (ans)

    x/20= C’s total work
    (x-2)/15= B’s total work
    2/12 = A’s total work
    (you can do such questions with approach)

  12. Deepika says:

    Hello friends I am from vocational Background but working really hard from SSC preparation. Please hint me on the solving following time and work problems.
    1. If 5 men or 8 women can do a piece of work in 12 days, how many days will be taken by 2 men and 4 women to do the same work

    2. 15 women can do 1/2 work in 20 days. In how many days will 20 women do the full work?

    3. A and B can be a piece of work in 10 days and C and A in 20 days. C alone can do the work in `

    4.Two taps can separately fill a cistern in 6 and 7 minutes respectively. If the taps are opened turn by turn each for a minute, find the time taken by them to fill the cistern.

    • viren says:

      1st sol: since work is same apply speed*time-distance , so 5m*12w=8w*12,solve for 1 w=5/8m asks:2m+4w=days? Put 1w=5/8m n sol ve tht is 9/2m nw 5m do in 12 days n 9/2 m will do in 40/3 d ..its min whts urs

  13. Deepika says:

    i have solved 2nd

    • karna says:

      ans is 120?

  14. PRABHU says:

    nice stuff admin .thank u..

  15. Ranjith says:

    Hai, i have doubt on following question, please help me to solve quickly,

    A alone can complete a work in 16 days and B alone can do in 12 days. Starting with A, they work on alternate days. The total work will be completed in how many days?

  16. neha sharma says:

    Pls help me solve this question using above STD method
    A alone can complete work in 16 days and B alone in 12 days.Starting with A ,they work on alternate days.The total work will be complted in how many days?

  17. vinayak says:

    20 women can do a job in 20 days. after each day, a woman is replaced by a man is twice as efficient as a women on which day does the job gets completed??? anyone

    • viren chahal says:

      well ans-10 days..becz if each woman replaced by a man-tht mean 20 men,but efficiency is high time will be less.so half time in my opinion

  18. Narayan says:

    Respected sir, I was unable to solve following 2 problems from Time and work. It looks complicated to me. Plz,help.

    problem 1- B can do a job in 6 hrs.B and C can do it in 4 hrs, and A,B,C in 2*(2/3)hrs.In how many hrs can A and B do it? option (a)3*(3/4) (b)3*(3/7) (c)2*(3/7) (d)4*(3/7)

    problem 2- A and B can do a piece of work in 12 days.A and C together work twice as much as B, A and B together work thrice as much as C. In what time could each do it separately?

  19. ravi says:

    can any one solve the question by using STD table method
    urgent coz i got some confusion-”

    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 the job in:

  20. anil soni says:

    Question : 6 men can complete the electric fitting in a building in 7 days .how many days will it take 21 men to do the job?

    mob : 9799422423

  21. anil soni says:

    plz reply……………………..fast

  22. gothi says:

    how we calculate

    Remaining work=60w minus 15w=45w

    in 2nd Que explain above by mrunal sir.

  23. prateek says:

    easy method is take out efficiency
    let men no be =x
    and womwnen = y

    efficiency of 4m and 6w together = 100/8 = 12.5%
    efficiency of 3m and 7w together = 100/10 = 10 %
    so,
    4x+6y=12.5 – 1

    3x+7y= 10 – 2

    solving one and two u get y = 1/4% (efficiency of women per day)
    for 10 women multiply by 10 = 10/4%
    so number of days would be 100/10/4 = 40 days

  24. swati says:

    Thanks sir becoz of only u now m able to solve questions VERY easily…and concepts also get cleared. Thanku…

  25. Mudasir says:

    Mrunal sir,how to solve this problem?
    Two persons A and B together can do a work in 10 days.The same work can be finished in 18 days if A works alone for 12 days and B works alone for 6 days.find the time required for each of them to finish the work if they work alone?

  26. unique says:

    really u r einstein’s incarnation

  27. SH says:

    Thank you, you teach and explain in a way that is so simple yet very effective. I wish you all the best. Thanks again.

  28. viren chahal says:

    mrunal sir or any1 plz solv dis from rajesh verma..a certain persons cn dig a trench 200 m long ,20 m deep ,100 m broad.thn the same no of persons dig another trench 40 m broad 30 m deep in 60 days..find length of 2nd trench..explain step by step ..if possible unitary method..

    • kushboo says:

      ji i tried….but i didnt get…. if u got answer…pls explain me

  29. Altz says:

    Thanks a lot Mrunal.ORG :)

  30. M.vasuki says:

    Twelve men can complete a work in 8 days. Three days after they stated the work, 3 more men joined them. In how many days will all of them together complete the remaining work?

    • M.vasuki says:

      plz here me to solve the above problem in a simple way Twelve men can complete a work in 8 days. Three days after they stated the work, 3 more men joined them. In how many days will all of them together complete the remaining work?

      • rahul says:

        SOLUTION :-. APPLY STD TABLE
        MEN MEN MEN
        S 12 12 12 + 3 = 15
        T 8 3 60/15 = 4 DAYS
        D 12X8 = 96 36 96 – 36 = 60 ANS. 4 DAYS

        • rahul says:

          SOLUTION IS NOT SHOWING PROPERLY
          PUT UR e-mail id
          i will mail u solution

  31. sandeeep says:

    A,B and C can do a piece of work in 10, 12 and 15 days respectively. A leaves 5 days before the completion of the work and B leaves 2 days after A. the whole work lasts for

  32. gbenga says:

    if 5 men finish a work in 12days, how many days will it take 8 men to finish the same work?

  33. VISHNU AS says:

    In how many ways 4 letters can be placed in 4 envelops such that none of them are going to the right envelop?

  34. VISHNU AS says:

    Use time*efficncy = work
    Since work is same ,
    12*5=k*8…….find out k…

  35. raju says:

    A, B and C can finish a piece of work in 30, 40 and 60 days resoectively. 10 days after they started to work together B leaves. 4 days after B left, A leaves and C completes the remaining work. How many days C had worked altogether

  36. rakkhi says:

    4 men or 6women or 10 children can paint ahouse in 5 days the painting is given to a couple and 5 sons they finish the job in

  37. mukesh says:

    A can do a work in 10 days & B can do that work in 15 days. A & B both work together for 5 days. Rest of work is completed by C. They get rs 1500 for the work. How much salary B & C can get?

  38. VISHNU AS says:

    Find out the answer please

    There are 17 apples in a box. In how many ways we can distribute it to 3 people such that first person gets at least 1 , second gets at least 2and third gets at least 3..

    • Salman Qazi says:

      Hi Vishnu,

      Step 1 -> give 1 apple to 1st person , 2 apples to 2nd person and 3 apples to 3rd person.
      now you are left with 11 apples.

      each apple out of 11 can be distributed in 3 ways.

      so total no of ways -> 3 power 11

      • VISHNU AS says:

        Hi Salman
        But up to some part seems correct..
        Total no of ways not 3^11. , but it is 13C2..i think so..if wrong please excuse me

  39. kushboo says:

    11C3 ways=165 ways

  40. kushboo says:

    sorry ji 165 wrong

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