This document contains content from a website about time and work problems. It includes concept sessions, practice problems, and solutions related to topics like work efficiency, groups working together, and time taken to complete jobs. Practice problems cover scenarios involving individuals and groups of workers completing tasks in certain time periods. The solutions to each problem are provided.

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Time and Work
Concept Session 1 &
Practice Session

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Time and Work Basics
Groups at Work
Wage Distribution
Pipes and Cisterns
Chapter Pathway

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Time and Work Basics

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Work and Efficiency
𝑊𝑜𝑟𝑘 = 𝑇𝑖𝑚𝑒 × 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦
Amount of work
done per unit
time

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Always work with Efficiency
𝑡 𝐴 + 𝑡 𝐵 ≠ 𝑡 𝐴&𝐵
𝑒 𝐴 + 𝑒 𝐵 = 𝑒 𝐴&𝐵

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A takes 10 days to finish a job and B takes 20 days to finish the same job. In how
many days will A and B finish the work if they work together?
T&W Problems
Answer: 20/3

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P and Q can do a work in 15 days, Q and R can do the same work in 20 days and
P and R can do the same work in 12 days. If all three of them work together, in
how many days will the work be completed?
1) 6
2) 5
3) 10
4) None of these
T&W Problems
Answer: Option 3

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A can complete a work in 12 days, B in 15 days. Find the time they would take to
complete the work
1) When A and B work together on alternate days starting with A
2) When A and B work together on alternate days starting with B
3) If A joined the work two days after B started?
4) If B leaves two days before the actual completion of the work?
5) If A leaves two days before the scheduled completion of the work?
6) If B does negative work at the same rate?
T&W Problems

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Akbar takes 16 days to complete a job and Anthony takes D days to complete
the same job. Akbar and Anthony work on alternate days. If they take exactly
the same time irrespective of who starts the job, how many positive integer
values are possible for D?
1) 3
2) 4
3) 5
4) Cannot be determined
T&W Problems
Answer: Option 2

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Groups at Work

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Problems – Groups involving ‘and’
2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys
can do the same work in 8 days. In how many days can 2 men and 1 boy do
the work?
1) 13.5
2) 14.5
3) 11.5
4) 12.5
5) None of these
Answer: option 4

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Problems – Groups involving ‘or’
6 men or 10 boys can do a piece of work in 15 days. How many days will 12
men and 5 boys take to reap a field that is 4 times the area?
1) 6
2) 12
3) 15
4) 24
5) None of these
Answer: option 4

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Time and Work
Practice Session

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A can lay railway track between two given stations in 15 days and B can do the
same job in 20 days. With help of C, they did the job in 5 days. Then, C alone
can do the job in:
1) 12 days
2) 15 days
3) 10 days
4) 16 days
Practice Problems
Answer: Option 1

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8 men and 4 women together can complete a piece of work in 6 days. The work
done by a man in one day is double the work done by a woman in one day. If 8
men and 4 women started working and after 2 days 4 men left and 4 new
women joined, in how many more days will the work be completed?
1) 5 days
2) 8 days
3) 6 days
4) 4 days
Practice Problems
Answer: Option 1

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A, B and C can do a piece of work in 15, 30 and 60 days respectively. First day A
works alone, on the second day he is accompanied by only B and on the third
day he is accompanied by only C and on the fourth day A works alone, the next
day he is accompanied by only B, and the next day by only C. If they continue to
work in this fashion, In how many days will the work get over?
Practice Problems
Answer: 12

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A is thrice as good as workman as B and therefore is able to finish a job in 30
days less than B. Working together, in how many days can they do a similar job?
Practice Problems
Answer: 11.25

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A is thrice as good as workman as B and therefore is able to finish a job in 30
days less than B. Working on alternate days beginning with B, in how many days
can they do a similar job?
Practice Problems
Answer: 23

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A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while
A and C together can do it in 2 hours. How many hours will A and B take to do
the same work?
Practice Problems
Answer: 3

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Humans and robots can both perform a job but at different efficiencies. Fifteen
humans and five robots working together take thirty days to finish the job,
whereas five humans and fifteen robots working together take sixty days to
finish it. How many days will fifteen humans working together (without any
robot) take to finish it?
1) 36
2) 32
3) 45
4) 40
Practice Problems
Answer: Option 2
CAT 2018
(Morning Slot)