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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. 

 

 

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 

 

Model Questions

1. A can do a piece of work in 15 days, B can do it in 18 days. B started the work after 6 days B left and A joins 5 days after the work was started. The work has finished in...
A) 12 days            B) 17 days
C) 15 days            D) 9 days 

 

2. P can do a piece of work in 21 days. Q is 40 percent more efficient than P. Then in how many days the work gets completed when both are working simultaneously?
3
A) 10 days     B)
C)         D) 12 days

 

 

3. 20 men can complete a work in 12 days. 6 days after they started the work, 5 men left the job. How many days will it take to complete the remaining work?
A) 10            B) 7             C) 8             D) 6

 

4. 35 women earned Rs.105000 by working 20 days. How many men must work for 15 days to receive Rs.108000 provided the daily wages of a man is twice that of a woman?
A) 18 men          B) 20 men            C) 16 men             D) 24 men

 

5. P can complete three-fifth of the work in 6 days and Q can complete the one-fourth of the same work in 5 days. Then in how many days P and Q together complete the work?
A)           B)
C)           D)

 

 

6. A alone can do a piece of work in x days. B alone can do the same work in 5 days more than A. C alone can do the same work in 15 days. If all of them working together and 1 completed the work in days, then find 7 the value of ‘x’.
A) 20              B) 25              C) 30        D) 10

 

7. Kathir takes thrice as much time as Karthi and twice as much as Krish to finish a piece of work. Together they finish the work in 3 days. What is the time taken by Karthi to finish the work?
A) 10 days            B) 12 days           C) 6 days         D) 4 days

 

8. Preethi can complete the work in 24 minutes and Shri can complete the work in 36 min. 6 Kavitha can complete the work in ¾ th of efficient by both Preethi and Shri together. Find the total time taken by all together to complete the work.
A)          B)
C)          D)

 

9. Pipes p, q and r releases three different solution HNO2, HCl and HI. And these three pipes fill the empty tank in 25 minutes, 30 minutes and 40 minutes respectively. If all the pipes are opened, what is the ratio of HI in that mixed solution in tank after 5 minutes?
A)        B)        C)        D)

 

10. A and B together can do a work in 12 days, B and C can do together in 6 days while C and A together can do in 10 days. In how many days C alone will complete the work?
A)            B)
C)            D)

 

11. A tank has a leak which can empty a full tank in 28 minutes. A tap is turned on which can fill 2.5 liters a minute. The tank now becomes empty in 42 minutes. What is the capacity of the tank?
A) 210 liters              B) 342 liters
C) 140 litres              D) 230 litres

 

12. A and B undertake to complete a piece of work for Rs.1800. A can do it in 10 days, B can do it in 15 days and with the help of C they complete the work in 5 days. Find the share of C.
A) Rs.360               B) Rs.300           C) Rs.390          D) Rs.430

 

Key 

1-C  2-B  3-C  4-D  5-C  6-B  7-C  8-B  9-A  10-B  11-A   12-B

 

Explanations

Posted Date : 21-04-2022

గమనిక : ప్రతిభ.ఈనాడు.నెట్లో వచ్చే ప్రకటనలు అనేక దేశాల నుండి, వ్యాపారస్తులు లేదా వ్యక్తుల నుండి వివిధ పద్ధతులలో సేకరించబడతాయి. ఆయా ప్రకటనకర్తల ఉత్పత్తులు లేదా సేవల గురించి ఈనాడు యాజమాన్యానికీ, ఉద్యోగస్తులకూ ఎటువంటి అవగాహనా ఉండదు. కొన్ని ప్రకటనలు పాఠకుల అభిరుచిననుసరించి కృత్రిమ మేధస్సు సాంకేతికతతో పంపబడతాయి. ఏ ప్రకటనని అయినా పాఠకులు తగినంత జాగ్రత్త వహించి, ఉత్పత్తులు లేదా సేవల గురించి తగిన విచారణ చేసి, తగిన జాగ్రత్తలు తీసుకొని కొనుగోలు చేయాలి. ఉత్పత్తులు / సేవలపై ఈనాడు యాజమాన్యానికి ఎటువంటి నియంత్రణ ఉండదు. కనుక ఉత్పత్తులు లేదా సేవల నాణ్యత లేదా లోపాల విషయంలో ఈనాడు యాజమాన్యం ఎటువంటి బాధ్యత వహించదు. ఈ విషయంలో ఎటువంటి ఉత్తర ప్రత్యుత్తరాలకీ తావు లేదు. ఫిర్యాదులు తీసుకోబడవు.

 

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