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

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.

## So far 84 Comments posted

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.

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.

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!

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

Ans is 24 men

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?

Sorry friend my typing mistakes…

Ans is 48..

If u see my process…

Ur ans is right….

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

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…

36 days

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

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 days……………

Am i correct….??

its 48 required for the remaining work but 24 men already working so 24 more required

24 is the correct answer…….16 men are already working so 40-16= 24 ans