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

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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.

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

  1. 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.

  2. simple question but please answer

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

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