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

Aptitude91 Comments

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 Man1 Woman4 men & 6 women3 men & 7 women
Speedmw4m+6w3m+7w
Time810
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 Man1 Woman4 men & 6 women3 men & 7 women
Speedmw4m+6w3(11w)+7w
Time810
distance

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

1 Man1 Woman4 men & 6 women3 men & 7 women
Speedmw4m+6w40w
Time810
distance40w 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 Man1 Woman4 men & 6 women3 men & 7 women10 women
Speedmw4m+6w40w10w
Time810??
distance40w x 10= 400w400w

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 Man15 Woman
Speed12m15w
Time44
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 Man15 Woman6men
Speed12m15w6x (5/4)w
Time442
distance60w6x (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 Man15 Woman6menFind women
Speed12m15w6x (5/4)wFw
Time4423
Distance60w15w45w

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 kids8 men
Speed12k8m
Time1612
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 kids8 men16 men
Speed12k8m16m
Time16123
Distance8m x 12=96m16m 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 kids8 men16 menMen & kids
Speed12k8m16m6m+4k
Time16123??
Distance96m48m48m

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.





So far 91 Comments posted

  1. sunny kumar

    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. diptanshu gaur

      hey sunny 24 is the correct answer actually i use a different method for time & work questions acc. to my method 24 men finish the job in 16 days and 32 women did it in 24 days first take lcm of 16 and 24 as their respective speed to do the work ie: 48 (let 48 as total work that needs to be done) if we divide 48 by 16 then it is 3 thats the speed of 24 men in a day n same for women 2 is the speed now what will be the speed of 16 men that will be 2 because 24 and 16 divisible by 8 so speed of 8 men will be 1 16=2 & 24=3 same for women speed will be 16=1. the work has to be finished within 14 days if 16 men work for 14 days the total work done by them will be 28 becoz speed is 2 & women will do 14 work becoz speed is 1 now total work done=42 remaining 6 that is to be done so if 24 men can do 3 work in one day they will do 6 in two days so the remaining 6 they will contribute after 6 days. question is asking how main additional men required as well as other will also work for 2 days thankyou.

  2. Aanya

    Correct ans 24.
    1 man’s 1 day work =1/16*24, for woman it’s 1/32*24
    16 men 12 day work=16*12/16*24=1/2
    16 women 12days work=16*12/32*24=1/4
    Total completed work in 12 days=3/4
    Rest work=1/4
    16 men+ 16 women 1 day work= 16/16*24 + 16/32*24= 1/24+1/48=1/16
    Their 2 days work=1/8
    Extra men needed to complete the work=1/4-1/8= 1/8 in 2 days means 1/16 in one day
    24 men can complete a work in 16 days means their 1 day work 1/16, so we need 24 men.

    In writing it seems long but very quick when we actually solve!

  3. संकल्प

    24*16=32*24
    i.e.
    1M=2F

    so,
    16M+16F=24M
    find remaining work
    i.e 1- (12/16)=1/4th work remains
    now
    work- 1/4
    men- 24
    days- 2

    use relation WMT

      1. sunny kumar

        Thanks Sankalp!
        But could you plz help me with my solution given below-

        after M=2F OR F=M/2
        So, 8M + 16M
        24M *12 = 288M- Work done by 16M + 16F
        Work left to be done= (16*24M)- 288M
        = 96M

        Here on wards am facing the problem-
        as if 1M can do M work per day
        than to complete in two days why shouldnt it be 48M?

          1. Ashitha

            48 is required for remaining work is right. So men added is 48-24 = 24. Bcoz 24 are already working

  4. sunny kumar

    am also getting 48 as answer but the book m reffering, says 24.
    one more problem-

    25 men & 15 women can complete a work in 12 days.
    all of them start working together and after working for 8 days the women stops working.
    25 men completed the remaining work in 6 days
    how many days will it take for completing the entire job if only 15 women are put on the job?

    kindly help with this aswell…

    1. संकल्प

      Ans- 36 days (completing whole work by 15 female)
      How? Letsee…..

      Find remaining work that by both (25M+15F) i.e.
      12 – 8/12 = 1/3
      Nd
      This work done by 25M in 6 days,
      Find whole work done by 25M
      Nd
      Thats…18 days (i think u knows, how it is?)
      Nd
      Find 1D work of (25M+15F) as wel as 25M separately…
      Nd then find their difference…luklike….
      1/12 – 1/18 = 1/36

      So whole work done by 15F in 36D..

      Coss-check for examination…
      1/36 + 1/18 = 1/12………..12 days

  5. Garima

    Kindly help How to solve this type of Ques.
    8 Men complete the work in 12 days. 4 Women can complete the same work in 48 days while 10 children can complete same work in 24 days. In how many days 10 Men,4 Women & 10 Children complete the work?

  6. shakti

    1. 12 men take 18 days to complete a job where as 12 women in 18 days can com. 3/4th of the same job. how many days will 10m and 8 w together take to complete the same job?

  7. shivagi

    hi sankalp
    i want to ask how do u find work in the question asked by sunny kumar?
    i mean, i was doing it by very long multiplication – 24men*16 days= 384 m
    n u did sumthing like 1- 12/16 = 1/4
    so where does this 12/16 came from….
    how did u find the remaining work in jus 2 simple steps?

  8. SRaman

    can anyone solve this problem in STD method..

    6Men can complete apiece of work in 12 days. 8women can complete the same piece of work in 18 days, whereas 18 children can complete the piece of work in 10 days. 4men, 12 women and 20 children work together for 2 days. if only men were to complete the remaining work in 1 day. how many men would be required totally ?

  9. RAJBALA

    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?

  10. ashish kumar

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

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