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

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

# 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

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.

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

1. If 5 men and 6 women complete a work in 6 days,10 men and 4 women complete a work in 5 days, to how much time will 15 men and 9 women take ?
Sir can you please explain with easy steps.

1. (5m+6w)*6=(10m+4w)*5
30m+36w=50m+20w
20m=16w => 5m=4w
now time taken by 15m and 9women is (5m+6w)*6 /(15m+9w)
(4w+6w)*6 /(12w+9w)
10w*6/21w
60/21=20/7days

2. (5m+6w)*6 = (10m+4w)*5
on solving we get,
m=(4/5)w

distance= speed * time
distance= (10m+4w)*5
we know that,
m=(4/5)w
distance= (10*4/5 +4w)*5
distance= 60w

speed*time= distance
(15m+9w)*time =distance
(15*4/5 w +9w) * time = 60w
(12w + 9w) * time = 60w
time = 60w/21w
time = 20/7 days

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3. if five men cleared a portion of land for 4days, how many days will it take eight men to clear the same portion of land

1. 5men = 4 days
8men = x days

as men is directly proportional to days

5*4 = 8*x => x= 2.5 days

4. 1 old man or 2 girls or 3 boys can complete a work in 88 days. 1 old man, 1 girl and 1 boy together will do it in
can sum1 solve dis for me?

1. 1m=2g=3b=88 days.
So, 1 men’s per day work =1/88
Similarly, 1 girl=1/176
1boy=1/264
take the LCM and add 1/88+1/176+1/264=?
6+3+2/528 ie., LCM(88,176,264)
=11/528=1/48=48 days

5. Q- 8men can complete a piece of work in 4 days, 12 women can complete the same piece of work in 4 days, whereas 8 children can complete the same piece of work in 8 days. 2 men , 8 children , and 3 women were to finish the remaining work in 2 days, how many total women would be required?

kindly reply to this question in short

1. 8m =1/4
12w=1/4
8c=1/8
Therefore,per men,children and per women work is,
1m=1/32
1w=1/48
1c=1/64
Questions is…2m,8c,3w finishes the remaining work in 2 days.
total work =2*1/32+8*1/64+3*1/48 completes in 2 days.
i.e, 1/16+2/16+1/16=4/16=1/4th of the work in 2 days.So, 1 complete work in…
1/4=2=>1=2*4=8.
therefore total women required = 1/48*8=6 women.

2. 12 men and 18 women can reap a field in 14 days , then 8 men and 10 women can reap the same field in.

1. 12m+18w = 14
168m or 252w = 1 day
8m+10w
=8(1/168) + 10(1/252)
=1/21 + 1/126
=7/126
=1/18
8m +10w can reap a field in 18 days

6. 8 men and 4 women together can complete a piece od work in 6 days. The work done by a man in 1 day is double the work done by a woman in 1 day. If 8 men and 4 women started working and after 2 days 4 men left and 4 new women joined. In how much time the work will be complete?

7. 8 men and 4 women together can complete a piece of work in 6 days. The work done by a man in 1 day is double the work done by a woman in 1 day. If 8 men and 4 women started working and after 2 days 4 men left and 4 new women joined.In how much time the work will be complete?

8. If a machine can do a piece of work in 18 hours, how long will it take 3 machines

1. distance = distance
speed * time = speed * time
1 * 18 = 3 * time
18 = 3 * time
time = 18/3
time = 6

9. 32 men can complete a job in 70 days and 40 women in 72 days. 20 men started working and after 1/4th work was completed they were replaced by 48 women. In how many days was the whole work completed?

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11. 3men and 4women can do a piece of work in 10days. 2men and 5 women can do same piece of work in 12days.
Find how much days it require to do the same piece of work by women only.

8 men and 8 women can complete a job in 10 days. in how many days 10 women alone can complete it ?

13. 1 man or 1 woman or 1 child can do a piece of work in 69 days. Then in
How many days will 1 man 1 woman and 1 child will complete?

14. Rohan and sohan working on an assignment .rohan take 6 hour to type 32 pages and sohan take 5 hour to type 40 pages.how much time will they take,working together on two diffrent computers to type an assignment of 110 pages

1. 8.25 hours is the answer

Speed of Rohan, R= 32/6
Speed of Sohan, S =40/5

Now, total time taken by both of them for completing 110 pages will be, let x

so, new equation will be

R*x+S*x=110
x(R+S)=110
x(32/6 + 40/5)=110
x(16/3 + 8)=110
x((16+24)/3)=110
x=110*3/40
x=33/4 = 8.25

15. I have a question if 10men and 15women can complete the work in 6days.in how many days one women do the job

16. 7 men and 16 women do a work in 15 days then how many days need by 5 men and 8 women to complete the same work .
plz any one answer with proper methood plzz

17. 2 male,6 female,and 8 girls can do a work in 192 hrs,4 male and 16 girls can do it in 160 hrs,4 male and 6 female can do it in 240 hrs .10 male and 24 girls can do it in.

18. Ans…pls…15men,18women&24boys can do a work in 15 days.then how many days 18men,27women&36boys can do this work? Pls…..ans….