# Time and Work - Problems

### 1.  36 men can do a piece of work in 25 days. In how many days can 30 men do it?

Here , the work is same.. So,

(S X T) / W = (s X t) / w

= >       (S X T) / W = (s X t) / w    [ Cancel W for both sides]

Now, substitute the values...
= >  36 X 25  = 30 X t

= >  (36 X 25) / 30  =  t  => t = 900/3  =  30

### 2.  32 men can do a piece of work in 15 days working for 6 hours a day. In how many days will 40 men can finish it if they work for 8 hours a day?

32 X 15 X 6  = 40 X d X 8 = 9

### 3. If 16 men can build a wall of 52 m long in 25 days working for 8 hours a day, in how many days can 64 men build a similar wall of 260m long working for 10hrs a day?

As we know that (Strength X Time) / Work = 1 (Read details Here)

We can write =>

(16 * 200) / 52  =  (64 * X * 10) / 260

=>  X = 25

### 4. A man engaged 10 laborers to make 320 toys in 5 days. After 3 days he found that only 120 toys were made. How many additional men should he engage to finish the work in time?

here, equate the complete work with the remaining work

(10 X 3) / 120 = (10+X) x 2 / 200

= >   10+X = 25   =>   X = 15

### 5.  A can do a task in 20 days and B can do it in 30 days. In how many days can they finish it if they work together?

A's one day's work = 1/20

B's one day's work = 1/30

=> Their one day's work = (1/20)+(1/30)  =  (3+2)/60  =  5/60  =  1/12

This is their one day's work TOGETHER.
So, obviously the number of days will be = 12

Short Cut : calculate Product/Sum   =  (20 X 30) / 50 = 12 Thats it

### 6.  A, B and C can do a job in 20 days, 30 days and 60 days respectively. If they work together, in how many days will the work be finished?

(1/20)+(1/30)+(1/60) = (3+2+1)/60  =  6/60  = 1/10

So, the number of days is = 10

### 7.  Two taps A and B can fill a tank in 10 hours and 15 hours respectively. a third tap C can empty the full tank in 12 hours. How many hours will be required if all of them are opened simultaneously to fill in an empty tank completely?

Here, first two are Inlets and the last one is Outlet,

So,      (1/10)+(1/15)-(1/12) =  (6+4-5)/60  =  5/60  = 1/12

### 8. A and B can do a job in 12 days. B and C in 15 days and C and A in 20 days. In how many days can they finish it if they work TOGETHER?

A+B = 12
B+C = 15
C+A = 20

So here, A+B's One day's work = >   1/ (A+B) = 1/12

B+C's one day's work  =>  1/ (B+C) =  1/15

C+A's one day's work = > 1/(C+A) = 1/20

Just Add them  =>  1/( 2A+2B+2C)  =  12/60  =  1/5

=>  1/2(A+B+C)  =  1/5

=>1/(A+B+C)  =  1/10   [this is their one day's work TOGETHER]

So, they can finish it in 10 days :)

### 9.  A and B can do a job in 12 days. B and C can do the same job in 15 days. C and A in 20 days. In how many days can A alone finish the whole task???

A+B = 1/12
B+C = 1/15
C+A = 1/20

Here we need A, so take a pair which is NOT HAVING A  and subtract it from the others,

so,  A+B-(B+C)+C+A  =  A+B-B-C+C+A =  2A

But according to our Problem, 2A =  (1/12)-(1/15)+(1/20)
=>A = 1/30 (this is A's one day work but we need A's total work)

=> A = 30 Days

### 10. A and B can do a piece of work in 20 days. A alone can do it in 30 days. In how many days can B alone do it?

Per day work of A and B = 1/20

Work done by A=  1/30

So, B's one day work =  1/20  - 1/30  =  (3-2)/60  =  1/60
=>  B's work is 60 Days

Short Cut :   Product/diff  =  600/10  =  60  :)

That's all for now friends. All the best and Happy Reading :)

1. Admin,3rd quetion explanation is confusing,pls elaborate explanation

1. You might have confused with the number 200. Its the multiplication of 25 and 8.
And about the denominators in the first case our target is 52 m wall, in the second case 260 m wall. We equate both of them coz we know that the value of (Strength X Time ) / Work = 1

(if you know that X=1 and Y=1 then you can say X=Y no? same case here)

If still you are confusing plz let us know. We will update with another method. Good Day.

2. excellent mam

3. Really good one mam...

4. its reallly awesome

5. thank u mam. . it was really useful . . .

6. Mam in question number 9 plz explain 2A=(1/12)-(1/15)+(1/20) how this becomes 1/30... because when i calculate it as (1/12)-(1/15)+(1/20) = (5-4+3)/60 = 8/60... then how it becomes 1/30

7. Mam plz explain in question 9 How 2A=(1/12)-(1/15)+(1/20) becomes 1/30..
bcz (1/12)-(1/15)+(1/20)=(5-4+3)/60=4/60=2/30

8. panchali borthakurMarch 2, 2014 at 4:13 PM

5-4-3/60=2/60=1/30

9. 5-4+3/60 =1/15=2A => A =1/30

2. thanks..guide 4 bank exams

3. wats there to be confusing its crystal clear, just multiply 25*8=200
(16*25*8)/52=(64*X*10)/260
X=25

4. describe 4th problem how can u calculate that

1. 10 laborers workd for 3 days and made 120 toys...

10 laborers and some additional men SHOULD made the remaining 200 toys (320-120) in 2 days. So just equate those two equations. Read basics so that you can easily understand the process.

5. mam i hav no words for ur work..u r just awesome....i really felt difficult to solve these types of problems but now i can easily solve it..thnks alot....

Rishabh Kapoor

6. Really doing a great job. may god bless you ... plz describe the 9th problem. how that 2A and Divided by 4 appears here

1. First have a close look at 8th problem, so that you can easily understand the 9th one.

In the question, they've asked that "A's individual Work".. We dont know that. But we do know A+B's work, B+C's work and C+D's work.

so here our target to eliminate B and C... so we took that pair and subtracted from the remaining pairs...

Result =>

A+B-B-C+A+C

B and C got cancelled and two As are there => 2A

now equate this to A's total work per day (Simplified in the problem above with detailed steps. please have a look. And let us know if you still feel its difficult.

Good Day

2. Thank you :)

3. Thank you....

7. really superb mam

8. very easy to understand.Thank you mam

9. thanks4 bank guide. its excellent!thnak u mam

10. really a great job mam,thank u mam

11. shivani, you are really doing a gd job.....thank u 4 dat...really very helpful

12. grt job mam...... plz rectify d mistake in no. 6 as it will b confusing 4 other...... :((((((((

1. Sorry Priyanka. Its a typing mistake... Corrected it now... Thank you so much for the update

13. till now i felt TIME n WORK problems are difficult to solve..after learning this formula..it became easy..thank u mam:)

14. Sir, how to solve the problems of working on alternate days?

1. There is a shortcut method for those sort of problems Friend. Cant explain that here in comments section. We will try to update that method by next week.

15. Your work is quite appreciable as u n ur team is giving good, must say best material for concerning and go through. Keep going mam. Wish u n ur team a huge success.

16. Ur team is working precisely.

17. how excellent work u have done...thaxs mam for ur support its really nice ..
kiran

18. your work beyond expectation...thanks a ton..

19. is solve of problem 2 right??plz explain

20. sorry its right.i have used wrong number

21. Very usefull for bank exames....thanku mam

22. its very useful and easily understood by everyone mam.....thank you...

23. Very very useful,thank u very much

24. tricks are very useful........ thank u very much

25. Grt job upload more. G. . .

26. Helped me a lot...Thanks...

27. I can't understand example 4 can u plz explain me

28. 29. gr8 job admin whenever i got a job i must donate or help for your best service..but numb 4 is little bit confusing

30. plz provide the solution for the following....

A can do 3/4 of a work in 30 days.B can do 2/3 of a work in 20 days.In how many days can both of them complete it if they work together...?

31. Plz provide the solution for the following...

A can do 3/4 of a work in 30 days .B can do 2/3 of a work in 20 days .In how many days can both of them complete the work together?

32. To the question above A and B together can complete the work in (120/7) days or 17(1/7) days.
Solution: A requires 40 days to complete the task and B takes 30 days. So together they take 40*30/40+30 days.

33. Sir, can you explain the logic to solve the following problem
If 12 men and 16 boys can do a work in 5 days, 13 men and 24 boys do it in 4 days. In how many days can 7 men and 10 boys do it?

34. NICE NEED MORE EXPLANATION FOR Q.NO 4

35. NEED MORE EXPLANATION FOR 4

36. 37. pls sir giv explanation for qs no.6

38. Very nice...till now i felt these problem very tough to solve but after reading this nw m so happy dat m able to solve such kind of problems...
Thank u so much

39. its really good........

40. Actually, that Product/Sum formula is applicable only for problems having 2 persons ah !? you have applied that in 5th and 10th question ! Won't it be applicable for 6th sum having 3 persons ?!

1. There is another formula for 3 person

XYZ / (XY+YZ+ZX)

41. RESPECTED AUTHOR, PLZ INCLUDE SOME MORE PROBLEMS ON TIME AND WORK,

42. Prob No 8.

A+B's one day work =1/12
B+C= 1/15
C+A= 1/20

2(A+B+C) 's one day work =1/5

(A+B+C)'s one day work is = 1/10

So 10 Days.

43. A can do a piece of work 25 days and B in 20 days. After they worked together for 5 days, A goes away. The number of days required for B to complete the remaining work?

44. A can do a piece of work 25 days and B in 20 days. After they worked together for 5 days, A goes away. The number of days required for B to complete the remaining work?

45. can u pliz upload solution on problems relating to question, working on alternate days and on some tough questions. 10 q sir

46. really useful thank u

47. really useful thank u

48. These contents are very useful.
U r awesome.

49. plz can u give few more explms.....

50. can u please gve few more exmples....

51. Hi mam,
in 3rd example, u forget to write/multiply 8.

I should be 16*25*8 / 52 = 64*10*X/260
X=25
You have written the right answer

52. Hi,
In 1st example, no. of hours workedis not given So what do we consider the value for no. of hours?
.
As in 2nd example, no. of hours is given So u have multiply s*t*no. of hours worked.

53. too good, excellent....

54. Can u get the ans of 6th problem using the procedure of 5th problem i.e, (product/sum). If not what is the difference?

55. Thank u so much mam ..Great work..please add some different questions regarding pipes

56. super work madam....just one request please provide pdf files for all topics it is easy to take printouts

57. thank u sooooooo much madam... but one request madam please provide pdf for all topics it is easy to take printouts

58. Hello mam....I hv a problem...
Q- ajit can do as much work in2days as baljit can do in3days and baljit can do as much in 4 days as diljit in 5 days. A piece of work takes 20 days if all work together. How long would baljit take to do all the work by himself??

59. Hello mam, I hav a ques.
Q- ram can do as much work in 2days as baljit can do in 3days nd baljit can do as much in 4 days as diljit in 5days. A peice of work takes a 20 days if all work together. How long would baljit take to do all the work by himself??

60. thankuuu so much :)

61. very useful info... thnx

62. thank u for ur great work... after reading this method am able to solve this kind of problem...and one more help mam ...please solve the problem which is given below::45 man can complete a work in 16 days, 6 days after they started working, 30 more men joined them. how many days will they now take to complete the remaining work??? any shortcut for this problem,,,??pls help me i cant undestand this type of problem

63. i can't write any comment with my name..

64. Excellent work....super.....

65. a & b working togethr for 2hr & 3hrs and they complete half the work.. in work of next 3hrs they had to complete 1/20th work.. if b alone do work.. wen it ll complete

66. plz try to post more difficult questions for practising

67. 