# TIME AND WORK

* 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.

Previous and 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 Posted Date : 04-10-2021

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