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

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Mrunal Polity Lecture

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.

Mrunal recommends

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

  1. a completes a piece of work in 30 days . b and c can complets the same work in 40 days simultaneously and a and b can do the same work in 48 days. in how many days can c do the whole work alone?

    plzz solve this
    m confused?

    1. Your question is wrong. If A can complete the work in 30days how he can took 48days while working with B. that means B is doing negative work. So if C alone wants to complete the work,he cant. My suggestion here is read the question carefully and than apply common sense first to make a ground/equations, than apply math to solve it.

  2. 15 man and 15 women divided in 15 groups.how many rules to divided when each groups have 1 man and 1 women?

  3. plz
    provide solution of this question
    if 5 man and 9 woman do work in 19 days .than 6 man and 3 woman how much complete the work?

  4. A piece of work can be done by 3 men and 4 woman in6 days and 3 men and 1 woman in 8 days and by 4 boys and 8 woman in 5 days. how long does one boy take to complete the work single handed??

    plzz give full solution!!

    1. I think he can do that piece of work single handed within 15-20 min.

  5. three men can complete a piece of work in 18 days.6 boys also complete the same work in 18 days..how many days if 4 men and 4 boys together to finish the same work?please help for this question to answer in easy way

  6. 7 men can complete a piece of work in 12 days. How many additional men will be required to complete double the work in 8 days?

    pls give me answer with proper steps………..

    1. M1xD1xW2 = M2xD2xW1
      7×12×2=(7+Additional)×8×1
      168 = 56 + 8Additional
      8Additional = 112
      Additional = 14

    2. parth i have easy method to do these type of questions
      first of write down the value which we have to find here it is 7 men
      now we know work must be done in 8 days so more men are needed so according to rule of fraction 7 x 12/8
      again double the work means more men needed 7 x 12/8 x 2/1= 21 men
      subtract 7 u will get 14 as answer.

  7. You are the best teacher..

  8. A and B work together in 5 days..A use double efficiency and B use half efficiency and finish the work in 4 days togetherly.in how many days A alone can finish. the work…..sir pls.give me answer

    1. 10days. and A and B are equal.

  9. 12 days-1work-7men
    8days-2work-let x more man

    X/7=12/8*2/1

    21men
    We hv already 7 men so required 21-7= 14 men more

  10. A,B,C can complete a work in 24, 52,64 day respectively if they start the work togather and after 6 day a leave the work and b leave the work before 6 day to complete the work.in how many day work will complete

  11. Find the amount of rupees 2500 invested at 12% during the period from 4th feb 2014 to april 2015 ? Anyone ??

  12. 6 men and 11 women can complete a work in 30 days. 4 men and 6 women can complete the same work in 50 days.find in how many days 10 men, 5 woman and 10 children can do the same work of each women I twice as efficient as a child…?

  13. If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be
    A. 4 days B. 5 days
    C. 6 days D. 7 days

  14. If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be
    A. 4 days B. 5 days
    C. 6 days D. 7 days by std method please explain me i have made the table but the problem is i did not getting the concept to get the total distance covered in the end column case
    m=2b by putting all in the equations we get 50b in 15m+20b case
    , 18b in 6m+8b case and 52b in 26m+48b case what to to
    next always struck in getting the total distance for last column

    1. Ans is 4 days.
      Well, after getting m=2b, one gets 18b as the sum in 6m+8b case , multiply it with 10 to get the total work done which would be 200b. Further you need to solve the last column. You will get 50b in speed column. Now divide the total work which you have got from column 1 i.e 200b by 50b and you get t = 4 days.

  15. 12 men nd 8 women can do a price of work in 16 days, while 13 men nd 1 woman can do it in 18 days.
    How long will 13 men nd 12 women take to finish the work?

  16. 12 man and 18 ladies can do a work in 14 days, however 8 mans and 16 ladies how many days take for complete the work?’

  17. Help me for this question please
    ond qtn ide solve maadi aaytha
    2 men and three women can do a piece of work in 15 days. 4 men and 18 women can do the work in 3 3/4 days. in how many days can 10 men and 15 women together complete the work?

  18. 12 men take 18 days to complete a job whereas 12 women in 18 days can complete 3/4 of the same job. How many days will 10 men and 8 women together take to complete the same job?

    Kindly resolve this problem with explanation.

  19. Three men start together to travel the same way around a circular track of 11 km. their speed 4, 5.5, 8 kmph resp. when will they meet at the first starting point for the first time.
    1)After 11hr.2) after 21hr 3)after 22hr 4)after 33hr 5) none of these

  20. 12 men take 18 days to complete a job whereas 12 women in 18 days can complete 3/4 of the same job. How many days will 10 men and 8 women together take to complete the same job?

  21. A and B together can complete a piece of work
    in T days. If A alone completes the work in
    T + 3 days and B alone completes the piece
    of work in T + 12 days, what is T?

    Kindly explain this with the help of STD method…

  22. please solve

    10 men can finish a work in 15 days.8 women can finish the same work in 25 days.only 10 women started working and in few days completed certain amount of work.after that 3 men joined them.the remaining work can be be completed by 10 women and 3 men together in 5 days.after how many days 3 men joined 10 women

  23. A and B together can complete a work in 3 days. They started together but after 2 days,B left the work. if the work is completed after 2 more days,B alone could do the work in how many days?

  24. If 5men & 9women complete a work in 19 days. In how many days 3men & 6women complete the same?

  25. A+B both for 2 days = 1/3*2 work
    So, work left = (1- 2/3)
    =1/3
    Now as B left the work and the left over work was done in 2 more days, it means A did the the work.
    So, 1/3 work/2days = 1/6 is A’s 1 day’s work.

    (A+B) – A = B’s 1day’s work.
    (1/3 – 1/6) = 1/6
    Hence, B alone could do the work in 6 days.

  26. one man started a project on the first day. one man joins on each days from the second day. The project will be completed in exactly 20 days. instead, if a team of 7 men work regularly, the work completed in exactly n days. what is n.

    Please solve this question

  27. Is n = 57.14? I’m not sure.

  28. Sunny 48 men are required if we have to complete it in 1day. So, divide total men by two. 24 is answer.

  29. Please solve this
    8 men can complete a work in 5 days. 12 women can complete in 10 days and 10 children in 24 days. 1 man, 1 woman and 1 child started the work. In how many days will the work get completed if the man did twice the work as woman and also twice the work as child?

  30. Can someone please help me to solve this problem: A,B & C working together can complete a work in 8 days, all three started the work together by C quit after working for 2 days if remaining work is completed by A & B in 9 days then in how many days C alone complet the total work?

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