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Solved Examples(Set 1) - Time and Work

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. 7/15B. 11/15
C. 2/11D. 8/15
Discuss
answer with explanation

Answer: Option D

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. P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?
A. 9(1/5) daysB. 9(3/5) days
C. 9(2/5) daysD. 10 days
Discuss
answer with explanation

Answer: Option B

Explanation:

Amount of work P can do in 1 day = 1/16
Amount of work Q can do in 1 day = 1/12

Amount of work P, Q and R can together do in 1 day = 1/4

Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 - 1/12 = 5/48

=> Hence R can do the job on 48/5 days = 9 (3/5) days

3. 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. 15 daysB. 9 days
C. 10 daysD. 14 days
Discuss
answer with explanation

Answer: Option A

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

4. 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. 22 ½ daysB. 18 days
C. 26 daysD. 24 days
Discuss
answer with explanation

Answer: Option A

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

5. A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?
A. Rs. 600B. Rs. 420
C. Rs. 400D. Rs. 380
Discuss
answer with explanation

Answer: Option C

Explanation:

Amount of work A can do in 1 day = 1/6
Amount of work B can do in 1 day = 1/8

Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24

Amount of work A + B + C can do = 1/3

Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24

work A can do in 1 day: work B can do in 1 day: work C can do in 1 day
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1

Amount to be paid to C = 3200 × (1/8) = 400

Comments(184)

profileAnil Peshin
2015-06-26 14:28:14 
In Question no.7, you should ask in how many HOURS will B complete the work, not in how many DAYS because the answer is in Hours (12) not in days. Please slightly modify the statement, if correct
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profileSupport Team, careerbless.com
2015-06-27 17:37:01 
Thanks Mr.Anil Peshin for pointing this out. It is corrected.
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profilevarsha sharma
2015-04-07 18:20:54 
A and B can complete their work in 5 days..A use his double efficiency and B use his half efficiency and complete their work in 4 days..in how many days A alone complete the work
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profileDev
2015-04-08 20:55:48 
Let work done by A in 1 day = a  (when working in normal efficiency)
and work done by B in 1 day = b (when working in normal efficiency)
Work done by A  and B in 1 day = 1/5
a + b = 1/5 ----(1)

Work done by A in 1 day (in double efficiency) = 2a
Work done by B in 1 day (in half efficiency) = b/2
Work done by A and B in 1 day (A in double efficiency and B in half efficiency) = 1/4
2a + b/2 = 1/4
8a + 2b = 1 ----(2)

Solving (1) and (2)
from (1) 2a + 2b = 2/5 ----(3)
(2)-(3) : 6a = 3/5
a = 3/30 = 1/10

Work done by A in 1 day = 1/10 (when working in normal efficiency)
A alone complete the work in 10 days when working in normal efficiency.
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profileAnup
2015-04-02 14:35:05 
A can do a piece of work in 14 days which B can do in 21 days .They begin together but 3 days before COMPLETION of the work ,A leaves off. In how many days B will complete remaining work??
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profileDev
2015-04-08 18:06:06 
I think question is wrong. 3 days before COMPLETION of the work ,A leaves off. i.e., work will be completed in 3 days after A leaves?

Probably question is to find out the total number of days in which the work will get completed

Work done by A in 1 day = 1/14
Work done by B in 1 day = 1/21
Work done by A&B in 1 day = 1/14 + 1/21 = 5/42
B works alone in the last 3 days and completes 3*1/21 = 1/7 of the work.
Remaining work = 1 - 1/7 = 6/7
Time taken by A&B to do this 6/7 of the work = (6/7)/(5/42) = 36/5 = 7.2
Total days needed to complete the work =  7.2+3=10.2 days
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profileazhar
2015-11-25 06:38:45 
in the above problem the question is asking about time taken by B to complete remaining work not about total time required...
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profilesam
2015-12-23 11:40:48 
@azhar, time taken by B to complete remaining work is 3 days which is given in the question, isn't it?
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profileamit
2015-04-01 09:36:17 
20 men can complete a task in 40 days. If after every five days two men left. In how many days the work will be completed?
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profileVishal Bhatnagar
2016-08-14 12:22:57 
20*40 = 800
So
20*5 = 100, 18*5= 90, 16*5 = 80, 14*5 =70, 12*5 = 60, 10*5 = 50, 8*5 = 40, 6*5 = 30, 4*5 = 20, 2*5=10
Total 100+90+80+70+60+50+40+30+20+10 = 550 & still 250 work is incompleted so no worker no work.
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