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.
![[Reasoning] Calendar Questions: Finding day or date, concepts, shortcuts explained](https://mrunal.org/wp-content/uploads/2013/01/i-lr-500x383.png)
A,B and C can do a piece of work in 10, 12 and 15 days respectively. A leaves 5 days before the completion of the work and B leaves 2 days after A. the whole work lasts for
if 5 men finish a work in 12days, how many days will it take 8 men to finish the same work?
In how many ways 4 letters can be placed in 4 envelops such that none of them are going to the right envelop?
Use time*efficncy = work
Since work is same ,
12*5=k*8…….find out k…
A, B and C can finish a piece of work in 30, 40 and 60 days resoectively. 10 days after they started to work together B leaves. 4 days after B left, A leaves and C completes the remaining work. How many days C had worked altogether
4 men or 6women or 10 children can paint ahouse in 5 days the painting is given to a couple and 5 sons they finish the job in
A can do a work in 10 days & B can do that work in 15 days. A & B both work together for 5 days. Rest of work is completed by C. They get rs 1500 for the work. How much salary B & C can get?
Find out the answer please
There are 17 apples in a box. In how many ways we can distribute it to 3 people such that first person gets at least 1 , second gets at least 2and third gets at least 3..
Hi Vishnu,
Step 1 -> give 1 apple to 1st person , 2 apples to 2nd person and 3 apples to 3rd person.
now you are left with 11 apples.
each apple out of 11 can be distributed in 3 ways.
so total no of ways -> 3 power 11
Hi Salman
But up to some part seems correct..
Total no of ways not 3^11. , but it is 13C2..i think so..if wrong please excuse me
11C3 ways=165 ways
sorry ji 165 wrong
Dear mrunal,
Where are the other articles on Time n Work…its not there in the aptitude articles list..kindly upload them as they were very useful to us ..
Thank you
@case-2:
12M can do in 4Days => 1M can do in = 12*4 =48
15W can do in 4Days => 1W can do in = 15*4 = 60
so men starting work 2 Days then they left and women worked 3 Days for completing remain work.then we want to know no of women
(6*2/48) + (3*x/60) = 1………………=> x = 15
here x = no of women
6*2 = 6 men worked for 2 days then they left
3*x = x women worked for 3 days for completing remain work
1/48 = 1 Day work of man
1/60 = 1 Day work of woman
@ case-1:
4 men + 6 women = 8days
3 men + 7 women + 10 Days
man 1 day work = 1/m = x
woman 1 day work = 1/w = y
then 4 men and 6 women 1 day work = 1/8
3 men and 7 women 1 day work = 1/10
4x + 6y = 1/8………………(a)
3x + 7y = 1/10……………..(b)
multiply (a) with 3 and (b) with 4 then solve we will find y = 1/400
y = 1/w = 1/400 => 10 women = 10/w = 10/400 => 10/w = 1/40 (10 women complete the work in 40 Days)
@ case-3
12 children complete a work in 16 Days => 1 child 1 day work = 1/(12*16)
8 adults complete same work in 12 Days => 1 adult 1 day work = 1/(8*12)
16 adults worked 3 days and remaining work completed by {16-10(10 adults left after 3 Days) = 6}
6 adult + 4 children in x Days
{(16*3)/(8*12)} + x{ (6/8*12) + (4/12*16) }= 1
=> => 1/2 + x (1/16 + 1/ 48) = 1
=> => x = 6 (6 adults + 4 children completed in 6 Days)
Nice explanation.I have passed eight years to understand it ,but i can’t understand how to solve this type of questions.I am very thankful to you for such a nice tips.I am now able to solve such a question easily.too much easy.Thanks from heart.Please suggest me any book related to it which contain such a nice easy understand tips.Hoping for reply.
Thanks
Hi mrunal, i was learning this particular questions from time & work using my mobile. The tables u made are appearing vertically & not horizontally. This becomes difficult to understand what u’ve explained. The same problem was there in the recent current affairs articles also. This change happened recently only. U might ve changed the settings i guess. For gs current affairs it is okay to read. But in QA problems it is difficult to read the table vertically. I dono whether this problem is only with my mobile or others also. If possible plz change it. Thanks…
A can do work in 24 days, B can do in 30 days, C can do in 36 days. If A starts working with B and C alternatively, in how many days work will be completed? Plz solve
thank u so much for finding me the solution related to work problem
thankyou!
if 3 men and 4 boys can complete a work in 5 days, in how many days would 7 men and 6 boys complete the same work?
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.
hii Sunny,
in the last sentence of ur qn is how many men more to be added to complete the work. It means 24 men is already working, how many more men should be added…
So, its (24M+X) men has to do 96M work in 2 days
so 24M+X = 96M/2
24M+X=48M
X=48M-24M
i.e, x=24 men more needed to work…
4 men or 6 women or 10 children can print a house in 5 days. the painting is given to a couple and their 5 sons.they finish the job in?
hi sunny at first i also got the answer what u have got!!!!!!! ,Now see
given that 24 men can do a work in 16 days,
so now one man can do 1/24*16 work in one day,which is 1/384,
now the total work done by men is 384.
then given that 32 women can do a work in 24 days,
so now one woman can do 1/32*24 work in one day which is 1/768,
this clearly shows a men can do double the work of woman.
given that 16 men 16 woman worked for 12 days,
so now 16 woman’s work can be done by 8 men.
so now consider there are 24 men to work for 12 days.
now take the whole (12+2) days,then the work done is
W.D = no of men * no of days, so W.d =24 *14
=336
we have found above that the total work done by men is 384.
so remaining work is (384-336) = 48
now they are asking how many more men are needed to do the remaining work in 2 days
so w.d=48 and no of workers = x and no of days = 2,then
W.D = no of workers * no of days
48 = x * 2 , so x = 24
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
good job
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
36 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….??
1 1/11 Days Or 12/11 Days
8M=12 days
i.e 96M will do it in 1 day
same goes for women and children just multiply 8 with 12 u will get how many people u need for 1 day
then equalise it like 96m=192w
it will give us m/2
in children m/2.5
place those values u will have to find days for 16 MEN
more men means less days so according to rule of fraction put days value first 12x 8/16=6 days
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
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?
13 1/2 or 27/2 Days
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?
24 men takes 16 days
32 women takes 24 days.
now LCM between 16 and 24 gives 48.
lets take the total work is eating 48 pizzas.
so
24 men can eat 3 pizzas/day
32 women eats 2 pizzas/day
now from the above data we can tell
16 men can eat 2 pizzas/day
16 women can eat 1 pizza/day
so if 16 men and 16 women are eating for 12 days , the total amount ate is 36 pizzas. i.e (2+1) pizza per day * 12 days= 36 pizzas
now the remaining pizzas to be eaten is 12. i.e 48-36=12.
this has to be finished in 2 days.
so in 2 days 16 men and 16 women would be able to eat 6 pizzas.
now the remaining is 12-6= 6, which is to be eaten by some x-men in two days.
i.e 3 pizzas per day.
we know that 24 men can eat 3 pizzas per day. (refer 6th line of this post)
thus the answer is 24 x-men.
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 ?
Ans 24 men a…???
36 Days