Time and work session 1

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Time and Work
Concept Session 2 &
Practice Session

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

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Wage Distribution

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Work and Efficiency
𝑊𝑎𝑔𝑒 𝐴
𝑊𝑎𝑔𝑒 𝐵
=
𝑊𝑜𝑟𝑘 𝐷𝑜𝑛𝑒 𝐴
𝑊𝑜𝑟𝑘 𝐷𝑜𝑛𝑒 𝐵
When time taken is constant,
𝑊𝑎𝑔𝑒 𝐴
𝑊𝑎𝑔𝑒 𝐵
=
𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 𝐴
𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 𝐵

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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 the total money earned by
them.
1) 300
2) 360
3) 240
4) 420
T&W Problems
Answer: option 2

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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.).
2700
2500
3000
3200
T&W Problems
Answer: Option 1

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Pipes and Cisterns

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Pipes and Cisterns
In a tank there is a leak at 3/4th of he height above the base which can
empty the tank up to its height in 6 hours. There are two filling pipes which
can fill the tank in 6 and 12 hours respectively. How much time does it take
to fill the tank if both the pipes are opened and the leak is left uncorked. [in
hours]
1) 3
2) 4
3) 4.2
4) 4.5 Answer: option 3

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Pipes and Cisterns
In a tank there are two taps which can fill the tank in 6 hours and 12 hours.
At the time when the tank should have been full, it was observed that the
tank is only 3/4th full due to a crack at the bottom. In how much time the
crack could have emptied the full tank? [in hours]
1) 12
2) 15
3) 18
4) 16
Answer: option 4

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If A and B together take 𝑡 days to complete the work, A takes 𝑡 + 𝑎 days, B takes
𝑡 + 𝑏 days to do the same work, then the value of t can be calculated as
𝑡 = 𝑎𝑏
Concept

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Time and Work
Practice Session

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Two pipes A and B attached to a swimming pool can fill the pool in 20 minutes
and 30 minutes respectively working alone. Both were opened together but
due to malfunctioning of motor of pipe A, it had to be shut down after four
minutes but B continued to work till the swimming pool was filled completely.
Find the total time taken to fill the pool.
1) 20 mins
2) 22 mins
3) 24 mins
4) 18 mins
Practice Problems
Answer: Option 3

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Three pipes A, B and C were opened to fill a cistern. Working alone, A, B and C
require 12, 15 and 20 minutes respectively. After 2 minutes of working
together, A got blocked and after another 3 minutes, B also got blocked. C
continued to work till the end and the cistern got completely filled. What is the
total time taken to fill the cistern ?
10
15
9
12
Practice Problems
Answer: Option 1

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Three pipes A, B and C were opened to fill a tank. Working alone, A, B and C
require 10, 15 and 20 hours respectively. A was opened at 5 AM, B at 6 AM and
C at 7 AM. At what time the tank would be completely filled, given that pipe C
can only work for 3 hours at a stretch, and needs 1 hour standing time to work
again.
1) 10 : 00 PM
2) 10 : 30 PM
3) 11 : 30 PM
4) 11 : 00 PM
Practice Problems
Answer: Option 2

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P can do a piece of work in 18 days more than the time taken by P and Q
together. Q can do the same work in 8 days more than the time taken by P and
Q together. They take up a work for a total compensation of Rs. 36000 and with
the help of R complete it in 10 days. What is R’s share of the compensation?[in
Rs]
1) 6000
2) 3000
3) 4500
4) 9000
Practice Problems
Answer: Option 1

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There are 12 pipes attached to a tank. Some of them are filling pipes and some
are draining pipes. Each of the fill pipes can fill the tank in 12 hours, while each
of the drain pipes will take 24 hours to drain a full tank completely. If all the
pipes are kept open when the tank was empty, it takes 4 hours for the tank to
overflow. How many of these pipes are draining pipes?
Practice Problems
Answer: 6

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A and B borrowed a tractor for 23 days. A ploughed 12 acres per day for a
certain number of days and then Bused it to plough 15 acres per day for the
remaining days. If they paid Rs 6,000 and Rs 4,000 respectively, for how many
days did B use the tractor?
Practice Problems
Answer: 8

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A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes
fill at the same rate, and all draining pipes drain at the same rate. The empty
tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on,
but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In
how many hours will the empty tank get completely filled when one draining
and two filling pipes are on?
Practice Problems
Answer: 10
CAT 2018
(Morning Slot)