1. A can do a piece of work in 20 days and B can do the same work in 45 days. In how many days both A and B together can do the work?
Sol:
Ans: D
2. Akhil is twice as good a workman as Bharath and is therefore able to finish a piece of work in 45 days less than Bharath. In how many days can they complete the whole work working together?
A) 20 days B) 30 days C) 35 days
D) 40 days E) 45 days
Sol:
Ans: B
3. 21 men can repair a road in 10 hours. How many men are required to repair the road in 7 hours?
A) 10 B) 15 C) 30 D) 25 E) 20
Sol:
Ans: C
4. A can write 21 pages in 7 hours and B can write 44 pages in 11 hours. If they write together, in how many hours can they write 126 pages?
A) 16 hours B) 24 hours C) 15 hours
D) 21 hours E) 18 hours
Sol: According to the question
Ans: E
5. A building is under construction and the task of paving the blocks is given to a group ofmen. 48 men can finish the given task in 24 days, working 6 hours/day. If 36 men take up the assignment and commit to finish it in 32 days, how many hours will they need to work per day?
A) 5 B) 6 C) 8 D) 10 E) 12
Sol: Formula Used :
M1 × D1 × H1 = M2 × D2 × H2
48 × 24 × 6 = 36 × 32 × H2
H2 = 6 hours
Ans: B
6. 25 men working 12 hours a day can complete a work in 30 days. How much time will it take to complete the work if 30 men are employed for 10 hours a day?
A) 40 B) 25 C) 30 D) 20 E) 15
Sol: Formula Used :
M1 × D1 × H1 = M2 × D2 × H2
25 × 30 × 12 = 30 × D2 × 10
D2 = 30 days
7. 36 people take 21 days to dig a pond. If the pond would have to be dug in 14 days, then the number of people to be employed will be?
A) 54 B) 45 C) 36 D) 72 E) 60
Sol: Formula used:
M1 × D1 = M2 × D2
36 × 21 = M2 × 14
M2 = 54
Ans: A
8. A and B can do a piece of work in 20 h, B and C can do it in 25 h, while A and C take 20 h to complete the work. B independently can complete the work in .... days.
A) 25 B) 50 C) 45 D) 40 E) 30
Sol:
Ans: B
9. 25 women can complete a piece of work in 12 days. If 5 more women are put on the job. In how many days will they complete the work?
A) 8 B) 9 C) 14 D) 10 E) 12
Sol: Formula used:
M1 × D1 = M2 × D2
25 × 12 = 30 × D2
D2 = 10
Ans: D
10. 11 men complete work in 12 days. If 6 men are employed, then the time required to complete that work will be....
A) 22 B) 20 C) 25 D) 30 E) 18
Sol: Formula Used :
M1 × D1 = M2 × D2
11 × 12 = 6 × D2
D2 = 22 days
Ans: A
11. 25 workers working for 6 h per day complete work in 10 days. If 30 workers are employed to work 5 h per day, what is the time required to complete the work?
A) 6 B) 8 C) 14 D) 12 E) 10
Sol: Formula Used :
M1 × D1 × H1 = M2 × D2 × H2
25 × 10 × 6 = 30 × D2 × 5
D2 = 10 days
Ans: E
12. A can do a piece of work in 16 days and B in 20 days. If they work on it together for 5 days, then the fraction of the work that is left is:
Sol:
Ans: D
13. 15 boys can complete a piece of work in 10 hours. In how many hours will 6 boys complete the same work
A) 20 B) 25 C) 30 D) 35 E) 40
Sol: Formula Used :
M1 × D1 = M2 × D2
15 × 10 = 6 × D2
D2 = 25 hours
Ans: B
14. 45 men can build a wall 250 m long in 15 days, working 9 hours a day. What will be the number of days that 50 men will take to build a similar wall 200 m long, working 6 h per day?
A) 16.2 B) 21.2 C) 25
D) 20 E) 19.6
Sol:
Ans: A
Directions (Qs. 1 - 13): Study the following questions carefully and choose the right answer:
1. Lallu is thrice as good a workman as Peelu and together they finish a piece of work in 27 days. The number of days taken by Lallu alone to finish the work is....
A) 25 days B) 22 days C) 32 days
D) 36 days E) None of these
2. Pawan can finish a work in 25 days and Ramesh can do the same work in 20 days. Ramesh worked for 12 days and left the job. In how many days, Pawan alone can finish the remaining work?
A) 5 days B) 10 days C) 15 days D) 17 days E) 8 days
3. Arun and Bhanu together can complete a particular task in 3 days. If Arun alone can complete the same task in 12 days. How many days will Bhanu take to complete the task if he works alone?
A) 9 days B) 7 days C) 5 days
D) 4 days E) None of these
4. Nirmal and Nirvan together can complete a piece of work in 8 days. If Nirmal alone can complete the same work in 32 days; in how many days can Nirvan alone complete that work?
5. 8 women can complete a piece of work in 10 days, whereas 12 children alone take 15 days to complete the same piece of work. How many days will 6 women and 10 children together take to complete the piece of work?
A) 7 B) 8 C) 6 D) 4 E) None of these
6. Anil, Bheem and Chay together earn Rs.350 per day, while Anil and Chay together earn Rs.230 and Bheem and Chay together earn Rs.240. The daily earning of Chay is...
A) Rs.40 B) Rs.68 C) Rs.120 D) Rs.150 E) Rs.180
Sol: Bheem's daily earning = Rs.(350 − 230)
= Rs.120
Anil's daily earning = Rs.(350 − 240)
= Rs.110
Chay's daily earning
= Rs.[350 − (120 + 110)] = Rs.120
Ans: C
7. 15 men and 10 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
A) 600 B) 500 C) 200 D) 225 E) 357
Sol: 1 man's 1 day's work
8. Sharat took 10 days to finish a piece of work. Mani takes 14 days to finish the same piece of work. Rajesh works twice as fast as Sharat. How many days will all three of them together take to finish the same piece of work?
9. A boy can do a job in 15 days, her mother takes 20 days and her sister finishes it in 25 days. How long will they take to complete the job if they are all together?
A) Less than 5 days B) Exactly 5 days C) Approximately 6.3 days
D) More than 6 days E) None of these
10. Arun and Bobby together can finish work in 10 days. Arun alone can finish the work in 14 days. In how many days will Bobby alone finish the work?
A) 24 B) 28 C) 32 D) 35 E) 50
Sol: If Arun and Bobby together can do a piece of work in x days and A alone can do it in y days, then B alone can do the work in
11. P completes a piece of work in 5 days and Q completes it in 7 days. If they both work on it together, then the number of days required to complete the same work in.....
12. Phani can complete a piece of work in 12 days. Phani and Bunny together can complete the same piece of work in 6 days. In how many days can Bunny alone complete the same piece of work?
A) 15 days B) 12 days C) 24 days D) 28 days E) 26 days
13. 3 workers Prakash, Rajesh and Pralabh can complete a piece of work in 6 days. Prakash takes 15 days less than Rajesh to complete the same work. Find in how many days will Pralabh complete the whole work alone with units 65% of his original efficiency, if Rajesh can complete the work alone in 35 days?
1. B is 50% more efficient than A. If A can complete 5/7th of a given task in 15 days, what fraction of the same task would remain incomplete if B works on it independently for 7 days only?
2. A project requires 12 women to complete it in 16 days, 12 women started working and after a few days from the start of the project, 4 women left. If the remaining project was completed in 18 days, in how many days the whole project was completed?
4. A is 25% less efficient than B. If A alone works on a given task for 16 days and is then replaced by B, who completes the remaining task in 6 days, in how many days can B alone complete the entire task?
A) 24 B) 18 C) 20 D) 16 E) 12
Sol: A : B = 75 : 100 = 3 : 4
A = 16 × 3 = 48
B = 6 × 4 = 24
total work = 72
5. Respective ratio between the efficiencies of A and B is 5 : 3. A alone can complete a work in 15 days. A started working alone and B joined the work after 2 days from the start of the work. In how many days will A and B together will complete 80% of the remaining work?
6. 16 men can complete a project in 20 days and 14 women can complete the same project in 30 days. 40 men started working on the project and they were replaced by 21 women after 5 days. In how many days these 21 women can finish the remaining work?
7. After completing 25% of a work P worked for 24 more days to complete the reaming work alone. Q is 20% less efficient than P. Both of them started the work together and completed 45% of the work. The remaining work is completed by Q alone, then find the total number days to complete the work?
A) 30 B) 40 C) 35 D) 15 E) 45
Sol: P can complete the 75% of work in 24 days. Then he can complete the total work in 32 days
8. If 12 workers can earn Rs.27000 in 9 days. Find the earnings of 8 workers in 6 days?
A) Rs.10000 B) Rs.12000 C) Rs.14000 D) Rs.15000 E) Rs.16000
9. A and B can do a piece of work in 16 days and 36 days respectively. For the first few days’ A and B worked together and then A left the work and C joined with B and C can complete the work 24 days alone. If the total work has been completed in 12 days, then find how many days did A and B work
together?
A) 4 B) 12 C) 7 D) 8 E) 5
10. Anshan and Raja together can do a work in 18 days whereas raja alone can do it in 72 days. If Bevy alone can do the same work in 40 days, and then find the ratio of the efficiency of Anshan to that of Bevy?
A) 5 : 3 B) 7 : 9 C) 13 : 8 D) 4 : 7 E) 16 : 9
11. A project can be completed by 12 women in 28 days. 7 women started working on the project. But after completing half of the work, they left and 10 men completed the remaining work. If the project was completed in total 32 days, in how many days 8 men will be able to complete the entire work?
A) 24 B) 30 C) 28 D) 20 E) 16
13. P and Q can complete the work in 5 days and Q alone can complete the same work in 10 days, then in how many days P alone can complete the total
work?
A) 7 days B) 8 days C) 10 days D) 15 days E) 12days
* If a man can do a piece of work in 5 days, then his one day’s work is 1/5.
* If a man can complete a piece of work in A days and another man can complete the same work in B days, then they together can complete the work in AB/A + B days.
* Similarly, three persons A, B and C together can complete in ABC/AB + BC + AC days.
* Men (Persons) and Time are inversely proportional i.e., when more men work, they take less time to complete the work. Similarly, when less men work, they take more time to complete the work.
* Men and Work are directly proportional i.e., when more men are there, they do more work and less men are there, they do less work.
* Similarly, Time and Work are also directly proportional. If men work for more time then they do more work and less time then the work is also less. Based on this the following formula can be drawn If M is Men (Persons), D is Days (Time) and W is work then
M1 × D1/W1 = M2 × D2/W2
MAN DAYS
No. of men to complete a work × No. of days they take = Man days
If 8 men can complete a work in 3 days, then the number of man days required to complete that work is 8 × 3 = 24.
Whatever may be the number of persons working on that, the total number of man days required for that work will be 24.
PIPES AND CISTERNS
The problems in pipes and cisterns are almost the same as those of Time and Work problems. In Pipes and Cistern, negative work in the form of leak or drain pipe will be there.
Pervious & Model Questions
1. A can complete a piece of work in 24 days. A and B together can complete the same work in 14.4 days. In what time does B alone complete that work?
A) 15 days B) 96 days C) 18 days D) 36 days
2. A can do a piece of work in 21 days. B can do the same work in 12 days. If B worked on the work for 8 days, how many days A worked on it?
A) 7 days B) 6 days C) 5 days D) 9 days
3. A and B do 3/5th part of a work and the rest of the work is completed by C. If A and C take the same work for Rs.5000 then what is the share of C (in Rs.) (SSC-CGL 2017)
A) 3000 B) 2500 C) 2000 D) 1500
4. A can do 3/4th of a work in 12 days and B completes the remaining work in 5 days. In how many days A and B working together can finish that work? 
5. A and B together can finish a work in 30 days. They worked for it for 20 days and then B left the work. The remaining work was done by A alone in 20 days more. In how many days can A alone finish the work? (SSC-CGL 2016)
A) 48 days B) 50 days C) 54 days D) 60 days
6. A is thrice as efficient as B and therefore able to complete the work 40 days less than B. In what time B alone can complete that work?
A) 60 days B) 20 days C) 40 days D) 25 days
7. If 10 people can do a job in 20 days, then 20 people with twice the efficiency can do the same job in ....... days (SSC-CGL 2016)
A) 5 B) 10 C) 20 D) 40
8. A and B can complete a piece of work in 15 days and 12 days respectively. They started working together and received an amount of Rs.5400. Find the share of B?
A) Rs.2400 B) Rs.1800 C) Rs.3000 D) Rs.3200
9. A, B and C can individually complete a task in 24 days, 16 days and 32 days respectively. If A and C start the work and worked for 6 days and left, then the number of days required by B to complete the remaining task is? (SSC-CGL 2019)
10. 24 men can reap 10 acres in 8 days. How many men are required to reap 15 acres in 6 days?
A) 32 B) 48 C) 56 D) 40
11. If 20 men working 8 hours per day can complete a piece of work in 21 days. How many hours per day must 48 men work to complete the same job in 7 days? (SSC-CGL 2016)
A) 12 B) 20 C) 10 D) 15
12. A, B and C can individually complete a task in 20 days, 16 days and 30 days respectively. If A and B started working on the task and they worked for 4 days and left, then the number of days required by C to finish the remaining task is ..... (in days) (SSC-CGL 2019) 
13. Two taps A and B can fill a tank in 25 minutes and 30 minutes respectively. A leak in the bottom of the tank can empty the tank in 50 minutes. When all the three are opened simultaneously, in how many minutes the tank is filled?
A) 5 min B) 12.5 min C) 18.75 min D) 15 min
14. A is 150% as good work man as B. if A can complete a work in 20 days, in what time both A and B together can complete that work?
A) 16 days B) 9 days C) 8 days D) 12 days
15. 26 men can do a piece of work in 12 days. In how many days can 39 men do that work?
A) 8 days B) 12 days C) 15 days D) 20 days
Key with Explanations
1-D; When two persons together working time and one of the persons working time is given, we can find other person's working
time by using a formula xy/x − y
⇒ 24 × 14.4/24 − 14.4 = 36 days
2-A;
3-C; Total work is 5 parts
As A & B completes 3 parts, C will compete 2 parts of work A and C do the same work (5 parts) for Rs. 5000
∴ Each part is Rs. 1000
∴ C will Receive Rs. 2000 for his 2 parts of work
4-D; A completes total work in 4/3 × 12 = 16 days
B completes total work in 4/1 × 5 = 20 days
A and B together complete the work in 
5-D; Work done by A and B = 1/30 × 20 = 2/3
Remaining work = 1 − 2/3 = 1/3
A completed 1/3 work in 20 days
∴ A can complete the total work in 3 × 20 = 60 days
6-A; A is thrice efficient means B takes three times time than A.
If A completes in X days, B can complete in 3X days.
∴ 3X − X = 40 days ⇒ 2X = 40 ⇒ X = 20
∴ B can complete in 3 × 20 = 60 days
7-A; If 10 men do the job in 20 days, 20 men can do in 10 days. When the efficiency of 20 men is double, the take half the time i.e., 5 days
8.C; Ratio of their one day's work = 1/15 : 1/12 = 4 : 5
∴ B's Share = 5/9 × 5400 = Rs.3000
9-A; A and C's in one day's work = 24 + 32/24 × 32 = 7/96
Work done by A and C in 6 days = 7/96 × 6 = 7/16
Remaining work = 1 − 7/16 = 9/16
Time taken by B to complete 9/16 work = 9/16 × 16 = 9 days
10-B; M1 = 24, D1 = 8, W1 = 10
M2 = X, D2 = 6, W2 = 15
M1 × D1/W1 = M2 × D2/W2
⇒ 24 × 8/10 = X × 6/15 ⇒ X = 48
11-C; Work done by 20 men = 20 × 8 × 21 Let 48 men done the work in 7 days working 'X' hours per day
Work done by 48 men = 48 × X × 7
∴ 20 × 8 × 21 = 48 × X × 7 ⇒ x = 10 hours
12-C; Work done by A and B in 4 days
= 20 + 16/20 × 16 × 4 = 9/20
Remaining work = 1 − 9/20 = 11/20
Time taken by C to complete 11/20 work
14-D; A is 150% efficient than B If A takes 100 days then B takes 150 days to complete that work.
But A can complete in 20 days 
