[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.

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1. sunny kumar

kindly help with below question-

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. SANDHYA

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…

3. rohit

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?

4. Surya Kumar .M

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

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. संकल्प

Ans is 24 men

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. संकल्प

Sorry friend my typing mistakes…
Ans is 48..
If u see my process…
Ur ans is right….

1. Ashitha

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

2. jose

good job

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. Virender Batra

36 days

2. 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

3. ABCD

36 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?

1. ANZ

6 days……………

Am i correct….??

2. ABCD

1 1/11 Days Or 12/11 Days

6. ashitha

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

7. Kanwaljeet Singh

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

8. 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?

1. ABCD

13 1/2 or 27/2 Days

9. 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?

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.

10. 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 ?

1. Sanju

Ans 24 men a…???

2. ABCD

36 Days

11. 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?

1. ashish

Your question is wrong. If A can complete the work in 30days how he can took 48days while working with B. that means B is doing negative work. So if C alone wants to complete the work,he cant. My suggestion here is read the question carefully and than apply common sense first to make a ground/equations, than apply math to solve it.

12. 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?

13. jeetendra kumar

plz
provide solution of this question
if 5 man and 9 woman do work in 19 days .than 6 man and 3 woman how much complete the work?

14. Raaz

A piece of work can be done by 3 men and 4 woman in6 days and 3 men and 1 woman in 8 days and by 4 boys and 8 woman in 5 days. how long does one boy take to complete the work single handed??

plzz give full solution!!

1. ashish

I think he can do that piece of work single handed within 15-20 min.

1. arul

45 days

15. preethi

three men can complete a piece of work in 18 days.6 boys also complete the same work in 18 days..how many days if 4 men and 4 boys together to finish the same work?please help for this question to answer in easy way

1. ABCD

9 Days

16. Parth

7 men can complete a piece of work in 12 days. How many additional men will be required to complete double the work in 8 days?

pls give me answer with proper steps………..

1. Sandroid

M1xD1xW2 = M2xD2xW1

17. Anas M

You are the best teacher..

18. varsha

A and B work together in 5 days..A use double efficiency and B use half efficiency and finish the work in 4 days togetherly.in how many days A alone can finish. the work…..sir pls.give me answer

1. ashish

10days. and A and B are equal.

19. var

12 days-1work-7men
8days-2work-let x more man

X/7=12/8*2/1

21men
We hv already 7 men so required 21-7= 14 men more

A,B,C can complete a work in 24, 52,64 day respectively if they start the work togather and after 6 day a leave the work and b leave the work before 6 day to complete the work.in how many day work will complete

21. Kundan

Find the amount of rupees 2500 invested at 12% during the period from 4th feb 2014 to april 2015 ? Anyone ??

22. saurabh

6 men and 11 women can complete a work in 30 days. 4 men and 6 women can complete the same work in 50 days.find in how many days 10 men, 5 woman and 10 children can do the same work of each women I twice as efficient as a child…?

23. siddharth

If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be
A. 4 days B. 5 days
C. 6 days D. 7 days

24. siddharth

If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be
A. 4 days B. 5 days
C. 6 days D. 7 days by std method please explain me i have made the table but the problem is i did not getting the concept to get the total distance covered in the end column case
m=2b by putting all in the equations we get 50b in 15m+20b case
, 18b in 6m+8b case and 52b in 26m+48b case what to to
next always struck in getting the total distance for last column

1. arti

Ans is 4 days.
Well, after getting m=2b, one gets 18b as the sum in 6m+8b case , multiply it with 10 to get the total work done which would be 200b. Further you need to solve the last column. You will get 50b in speed column. Now divide the total work which you have got from column 1 i.e 200b by 50b and you get t = 4 days.

25. Vaibhav

12 men nd 8 women can do a price of work in 16 days, while 13 men nd 1 woman can do it in 18 days.
How long will 13 men nd 12 women take to finish the work?

26. Parmdeep singh

12 man and 18 ladies can do a work in 14 days, however 8 mans and 16 ladies how many days take for complete the work?’

27. Lokesh

Help me for this question please
ond qtn ide solve maadi aaytha
2 men and three women can do a piece of work in 15 days. 4 men and 18 women can do the work in 3 3/4 days. in how many days can 10 men and 15 women together complete the work?

28. Ravi Prakash Srivastava

12 men take 18 days to complete a job whereas 12 women in 18 days can complete 3/4 of the same job. How many days will 10 men and 8 women together take to complete the same job?

Kindly resolve this problem with explanation.

29. Rajeswari

Three men start together to travel the same way around a circular track of 11 km. their speed 4, 5.5, 8 kmph resp. when will they meet at the first starting point for the first time.
1)After 11hr.2) after 21hr 3)after 22hr 4)after 33hr 5) none of these

12 men take 18 days to complete a job whereas 12 women in 18 days can complete 3/4 of the same job. How many days will 10 men and 8 women together take to complete the same job?

31. Jatin Arora

A and B together can complete a piece of work
in T days. If A alone completes the work in
T + 3 days and B alone completes the piece
of work in T + 12 days, what is T?

Kindly explain this with the help of STD method…

32. raja

10 men can finish a work in 15 days.8 women can finish the same work in 25 days.only 10 women started working and in few days completed certain amount of work.after that 3 men joined them.the remaining work can be be completed by 10 women and 3 men together in 5 days.after how many days 3 men joined 10 women

33. ujjwal

A and B together can complete a work in 3 days. They started together but after 2 days,B left the work. if the work is completed after 2 more days,B alone could do the work in how many days?

34. Pinky

If 5men & 9women complete a work in 19 days. In how many days 3men & 6women complete the same?

35. Sandroid

A+B both for 2 days = 1/3*2 work
So, work left = (1- 2/3)
=1/3
Now as B left the work and the left over work was done in 2 more days, it means A did the the work.
So, 1/3 work/2days = 1/6 is A’s 1 day’s work.

(A+B) – A = B’s 1day’s work.
(1/3 – 1/6) = 1/6
Hence, B alone could do the work in 6 days.

36. Gurpreet singh

one man started a project on the first day. one man joins on each days from the second day. The project will be completed in exactly 20 days. instead, if a team of 7 men work regularly, the work completed in exactly n days. what is n.

37. Sandroid

Is n = 57.14? I’m not sure.

38. Pratyush

Sunny 48 men are required if we have to complete it in 1day. So, divide total men by two. 24 is answer.

39. sahil

8 men can complete a work in 5 days. 12 women can complete in 10 days and 10 children in 24 days. 1 man, 1 woman and 1 child started the work. In how many days will the work get completed if the man did twice the work as woman and also twice the work as child?

40. Mansingh

Can someone please help me to solve this problem: A,B & C working together can complete a work in 8 days, all three started the work together by C quit after working for 2 days if remaining work is completed by A & B in 9 days then in how many days C alone complet the total work?

41. Sakshi

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. devendra

(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

42. somia

can anybody please tell me, where to get the art n culture pptx ???? in mrunal.org/download there are only economy n geography pptx. besides i am also not able to find the pptx of mrunal sir’s latest articles. if anybody knows kindly help..
Thanks.

43. samuel

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. mani

5men = 4 days
8men = x days

as men is directly proportional to days

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

44. mani

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?

45. rajesh

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

46. Sunil Kumar

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?

47. Sunil

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?

48. Johnp

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

49. Anitha. D

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?

50. abhay

Sir i need answer …one question in maths it irritats me a lot would u please give answer to me