This document contains 20 pages of content on the topics of time and work, pipes and cisterns, and wages and work. It includes definitions of key concepts, formulas, and example problems and solutions related to estimating work completed based on time and individual and group efficiencies. A variety of word problems are presented involving situations like groups of people or machines completing a fixed task together or separately over time, and pipes filling or emptying tanks at different rates. [END SUMMARY]

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Time and Work
Time and Work & Pipes and Cisterns

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Basic of Time and Work

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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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Problems
A takes 10 days to finish a job and B takes 15 days to finish the same
job. In how many days will A and B finish the work if they work
together?
1) 9
2) 8
3) 7
4) 6
5) None of these
Answer: option 4

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Problems
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) 11
5) None of these
Answer: option 3

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Problems
A and B together can do a piece of work in 6 days. If A can alone do
the work in 18 days, then the number of days required for B to finish
the work is
1) 12
2) 9
3) 15
4) 10
5) None of these
Answer: option 2
SBI Clerk
(2014)

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Problems
A can complete a piece of work in 18 days, B in 20 days and C in 30
days, B and C together start the work and are forced to leave after 2
days. The time taken by A alone to complete the remaining work is
1) 10 days
2) 12 days
3) 15 days
4) 16 days
Answer: option 3
SSC CGL
(2010)

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Problems
A is twice as good as B and together they finish a piece of work in 16
days. The number of days taken by A alone to finish the work is
1) 20 days
2) 21 days
3) 22 days
4) 24 days
Answer: option 4
SSC CGL
(2016)

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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 ‘and’
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
5) 9 days
Answer: option 1
IBPS PO
(2013)

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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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Pipes and Cisterns

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Problems
A tap can empty a tank in 30 minutes. A second tap can empty it in 45
minutes. If both the taps operate simultaneously, how much time is
needed to empty the tank?
1) 14 minutes
2) 30 minutes
3) 18 minutes
4) 15 minutes
5) None of these
Answer: option 3
SBI Clerks
(2014)

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Problems
There are 4 filling pipes and 3 emptying pipes capable of filling and
emptying in 12 minutes and 15 minutes respectively. If all the pipes
are opened together and as a result they fill 10 litres of water per
minute. Find the capacity of the tank.
1) 65 ltr
2) 70 ltr
3) 75 ltr
4) 80 ltr
5) None of these Answer: option 3
SBI PO Prelims
(2016)

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Problems
Pipe A can fill a tank in 20 minutes. Pipe B can empty it in 40 minutes.
Both were opened at noon on a certain day. After some time, B was
closed. A completed filling the remaining part of the tank. The tank was
full at 12.25 pm. Find the time at which pipe B was closed?
1) 12:05PM
2) 12:07PM
3) 12:10PM
4) None of these
Answer: option 3

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Wages and Work

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Problems – Wage proportional to efficiency
A and B can do a project in 12 and 15 days respectively. They were
told to complete the project in 5 days and were paid Rs. 1440. They
took the help of C and completed the work in time. Find C’s share(in
Rs.) in the total money earned by them.
1) 250
2) 360
3) 390
4) 450
Answer: option 2

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Problems – Wage proportional to work
A, B and C can complete a work in 10, 20 and 30 days respectively
when they work individually. All three started simultaneously. After 3
days A left, After two more days B left and C completed the remaining
work alone. If the total work is for Rs. 6000. Find the amount received
by C(in Rs.)
1) 2700
2) 2500
3) 3500
4) 550 Answer: option 1