CAT Problems on Time and Work PDF (Set-2):
Download CAT Problems on Time and Work (Set-2) PDF. It is the most important topic in CAT.
Question 1: A fill pipe can fill the tank in 15 minutes and a drain pipe can drain the tank in 30 minutes. If a system of ‘x’ pipes (includes both fill and drain pipes) fills the tank in 3 minutes. Find the possible value of ‘x’.
Question 2: A local train leaves Vijayawada for Guntur at 9:00 AM. The total distance from
Vijayawada to Guntur is 60 km. Another express train leaves for Guntur from Vijayawada, 10 minutes later. The speed of both the trains is 60 kmph. However, the local train has 19 uniformly spaced stops while the express train has 4 uniformly spaced stops. The trains stop at each stop for one minute and these stops do not include the destination. At what distance from Guntur will the second train overtake the first train? (Assume these two trains run on parallel tracks and no other trains run during this time)
a) 18 km
b) 21 km
c) 39 km
d) 42 km
Question 3: In a 200 m race, Abhay beats Chetan by 40m and Chetan beats Kundan by 20 m. If Abhay and Kundan were to run a 500 m race, then by what distance will Abhay beat Kundan?
Question 4: Ram can do a piece of work in 6 days while Shyam can do the same piece of work in 8 days. Ram and Shyam work together for 2 days and then Ram leaves the work while Shyam continues to work till the work gets completed. On which day from the beginning, will the work be completed?
Question 5: A group of certain number of men can complete a job in 5 days. On every alternate day starting from second day, 3 men are withdrawn from the job and on every alternate day starting from third day, 2 men are added to the job. If the job is completed in 6 days, what is the number of persons who started the job?
d) Cannot be determined
Question 6: A and B ran a race of 200 m from point X to point Y. A defeated B by 20 m. They decided to compete again but this time they decided that A would run from 5 m further behind X and B would run from a point 15 m ahead of X. Who would win the race in this case?
a) It will be a tie
b) A will win by 0.5 m
c) A will win by 1 m
d) B will win by 1 m
Question 7: Ashok can complete one-fourth of a piece of work in 6 days, Shiva can complete one-third of the same work in 8 days and Rahul can complete one-fifth of the work in 4 days. Ashok, Rahul, and Shiva start working on the work together for 5 days after which Ashok and Rahul stop working. How many days more would Shiva take to complete the work?
Question 8: The ratio of efficiencies of Mohan and Shyam is 2:3. The ratio of the time taken by Shyam and Anil to complete some work is 1: 3. If all three work together to finish a particular work, the work is completed in 24 days. How much time will it take to finish the same work if Mohan and Anil work together?
Question 9: An inlet pipe can fill a tank in 8 hours. An outlet pipe can empty the same tank in 12 hours. Initially the tank is completely empty. At this point of time, the inlet pipe is connected to the tank. After 3 hours, the outlet pipe is also connected to the tank. After how much time from the beginning, will the tank be full?
a) 15 hours
b) 18 hours
c) 20 hours
d) 24 hours
e) 22 hours
Question 10: Ram can beat Shyam by 40 meters in a race. If Ram starts from a point which is 20 metres behind the start line and Shyam starts from the start line, Ram will still beat Shyam by 24 metres. What is the length of their race?
a) 100 m
b) 150 m
c) 200 m
d) 250 m
e) 500 m
Solutions for CAT Problems on Time and Work PDF:
1) Answer (D)
In a given time, one fill pipe cancels out two drain pipes, and we require 5 more fill pipes to fill the tank in 3 minutes. So the number of pipes would be in the form of 3x+5.
Among the given options only ‘14’ is in the form of 3x+5.
So the correct option to choose is D.
2) Answer (A)
The second train leaves Vijayawada, 10 minutes after the first train.
So it has to catch up a time of 10 min to overtake the first train.
The total number of stops of the first train is 20 and the total number of stops of the second train is 5 (including the destination).
So for every four stops of the first train the second train stops at one stop.
So for 3 stops in 4 stops the second train has the chance to catch up one minute.
So to catch up 10 minutes, the number of stops required will be, 4+4+4+1 = 13 stops.
But for the second train to overtake the first train, one more stop of the first train is needed.
So after 14 stops of the first train, the second train will overtake the first train.
After 14 stops, the distance to Guntur will be, 60-14*3 = 18 km.
3) Answer (C)
In the time that Abhay runs 200 m, Chetan runs 160m so the ratio of speeds of Abhay and Chetan is 5:4
In the time Chetan runs 200m, Kundan runs 180m. So the ratio of speeds of Chetan and Kundan is 10:9
Thus we can say that in the time that Chetan runs 160m, Kundan runs 160*9/10 = 144 m
Thus in a 200 m race, Abhay will Kundan by 56m. Thus in a 500 m race, Abhay will beat Chandan by 56*2.5 = 140m
4) Answer (A)
Let total amount of work to be done is 48 units. So Ram does 8 units of work in one day while Shyam does 6 units of work in one day. Together they will be able to do 14 units of work in 1 day. So in 2 days they will finish 28 units of work. Now remaining work is 20 units. If Shyam continues to work, he will finish the work on the [20/6] = 4th day.
So the work will be completed on the 4 + 2 = 6th day.
Hence the correct answer is option a.
5) Answer (C)
Let the number of men who worked on day-1 be ‘n’.
The number of people working each day starting from day-1 will be,
n, n-3, n-1, n-4, n-2, n-5.
This work is equal to the work done by ‘n’ men in 5 days.
So, 6n-15 = 5n => n = 15.
6) Answer (B)
In the time A ran 200 m B ran 180 m, during the first race.
So the ratio of speeds of A and B is 200:180 = 10:9.
In the second race the distance to be covered by A is 205 m.
In the time A covers 405 m B would cover,
205*(9/10) = 184.5 m.
But B has to run 185 m to finish the race.
So A defeats B by 0.5 m.
7) Answer (D)
Let the total amount of work be 120 units.
Ashok completed 1/4rd of the work i.e. 30 units of work in 6 days. Thus, the amount of work Ashok can complete in 1 day = 30/6 = 5 units
The amount of work Shiva completed in 8 days = 120/3 = 40 units
Thus, the amount of work done by Shiva in 1 day = 40/8 = 5 units
Similarly, the amount of work done by Rahul in 1 day = 24/4 = 6 units
The work done by all three of them in 5 days = (5 + 5 + 6) x 5 = 80 units
Thus, amount of work remaining = 120 – 80 = 40 units
Thus, the number of days taken by Shiva to complete the remaining work = 40/5 = 8 days
8) Answer (C)
The ratio of efficiencies of Mohan and Shyam is 2:3. So let Mohan does 2 units of work in a day while Shyam does 3 units of work in a day.
The ratio of time taken by Shyam and Anil is 1:3, so the ratio of efficiencies of Shyam and Anil is 3:1
=> Anil does 1 unit of work in a day
=> So when all 3 are working together, the total work done in one day = 3 + 2 + 1 = 6 units
Total work which they do = 6*24 = 144 units
Now if only Mohan and Anil are working, then they will finish 2+1 = 3 units of work in one day. So total time required for them to finish the work = 144/3 = 48 days.
9) Answer (B)
Let the volume of the tank be 48 l.
The inlet pipe fills 6 litres in 1 hour while the outlet pipe empties 4 litres in 1 hour.
For the first three hours only inlet pipe is connected, so it will fill 6*3 = 18 litres in those 3 hours.
Now after this both the pipes are operating simultaneously. So, effectively only 2 litres will be filled in 1 hour. We have 30 litres to fill. Hence time required = 30/2 = 15 hours.
Total time from the beginning to fill the tank = 3 + 15 = 18 hours
10) Answer (C)
Let the length of the race be l
In the time that Ram travels l metres, Shyam travels l-40 metres.
In the time that Ram travels l+20 metres, Shyam travels l – 24 metres.
From these two equations we can see that in the time that Ram travels 20 metres, Shyam travels 16 metres.
So for every 20 metres travelled by Ram Shyam will be left behind by 4 metres.
The final gap between Ram and Shyam is 40 metres, hence there has to be 10 intervals of such 20 metres.
Hence the length of the race is 20*10 = 200 metres