In these problems the number of persons, quantity of work done and time taken are important factors. Also time taken by a person depends on the efficiency of that person which comes into picture when different people do the work such as women, children do the work alongside the men. The problems related to time and work can be solved by two major approaches – ratio & proportions and unitary method. Let us proceed to find some formulae related to these questions.
Important Formulas  Time and Work
SOLVED EXAMPLES
1. P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?  
A. 8/15  B. 7/15 
C. 11/15  D. 2/11 
Answer : Option A
Explanation :
Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15
2. A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. B alone can complete the work in  hours.  
A. 12 hours  B. 6 hours 
C. 8 hours  D. 10 hours 
Answer : Option A
Explanation :
Work done by A in 1 hour = 1/4
Work done by B and C in 1 hour = 1/3
Work done by A and C in 1 hour = 1/2
Work done by A,B and C in 1 hour = 1/4+1/3 = 7/12
Work done by B in 1 hour = 7/12 – 1/2 = 1/12
=> B alone can complete the work in 12 hours
3. A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?  
A. 37 ½ days  B. 22 days 
C. 31 days  D. 22 days 
Answer : Option A
Explanation :
Work done by A in 20 days = 80/100 = 8/10 = 4/5
Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25  (1)
Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
Work done by A and B in 1 day = 1/15 (2)
Work done by B in 1 day = 1/15 – 1/25 = 2/75
=> B can complete the work in 75/2 days = 37 ½ days
4. P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. How many days does P alone need to finish the remaining work?  
A. 8  B. 5 
C. 4  D. 6 
Answer : Option D
Explanation :
Work done by P in 1 day = 1/18
Work done by Q in 1 day = 1/15
Work done by Q in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which P can finish the remaining work = (1/3) / (1/18) = 6
5. Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 110 pages?  
A. 7 hour 15 minutes  B. 7 hour 30 minutes 
C. 8 hour 15 minutes  D. 8 hour 30 minutes 
Answer : Option C
Explanation :
Pages typed by Anil in 1 hour = 32/6 = 16/3
Pages typed by Suresh in 1 hour = 40/5 = 8
Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3
Time taken to type 110 pages when Anil and Suresh work together = 110 × 3 /40 = 33/4
= 8 ¼ hours = 8 hour 15 minutes
6. P works twice as fast as Q. If Q alone can complete a work in 12 days, P and Q can finish the work in  days  
A. 1  B. 2 
C. 3  D. 4 
Answer : Option D
Explanation :
Work done by Q in 1 day = 1/12
Work done by P in 1 day = 2 × (1/12) = 1/6
Work done by P and Q in 1 day = 1/12 + 1/6 = ¼
=> P and Q can finish the work in 4 days
7. A work can be finished in 16 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is  
A. 1:3  B. 4:3 
C. 2:3  D. 2:1 
Answer : Option B
Explanation :
Work done by 20 women in 1 day = 1/16
Work done by 1 woman in 1 day = 1/(16×20)
Work done by 16 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15×16)
8. P,Q and R together earn Rs.1620 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?  
A. Rs.40  B. Rs.70 
C. Rs.90  D. Rs.100 
Answer : Option B
Explanation :
Amount Earned by P,Q and R in 1 day = 1620/9 = 180 (1)
Amount Earned by P and R in 1 day = 600/5 = 120 (2)
Amount Earned by Q and R in 1 day = 910/7 = 130 (3)
(2)+(3)(1) => Amount Earned by P , Q and 2R in 1 day
 Amount Earned by P,Q and R in 1 day = 120+130180 = 70
=>Amount Earned by R in 1 day = 70
Ratio of the capacity of a man and woman =1/(15×16) : 1/(16×20) = 1/15 : 1/20
= 1/3 :1/4 = 4:3
9. P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?  
A. 10 days  B. 14 days 
C. 15 days  D. 9 days 
Answer : Option C
Explanation :
Amount of work P can do in 1 day = 1/20
Amount of work Q can do in 1 day = 1/30
Amount of work R can do in 1 day = 1/60
P is working alone and every third day Q and R is helping him
Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5
So work completed in 15 days = 5 × 1/5 = 1
Ie, the work will be done in 15 days
10. A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in  days if they work together.  
A. 18 days  B. 22 ½ days 
C. 24 days  D. 26 days 
Answer : Option B
Explanation :
If A completes a work in 1 day, B completes the same work in 3 days
Hence, if the difference is 2 days, B can complete the work in 3 days
=> if the difference is 60 days, B can complete the work in 90 days
=> Amount of work B can do in 1 day= 1/90
Amount of work A can do in 1 day = 3 × (1/90) = 1/30
Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45
=> A and B together can do the work in 45/2 days = 22 ½ days
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