CAT workshop 6- Time, Speed & Distance

Question: A monkey starts climbing a 15 feet tree. Each hour, he climbs 3 feet and rests for 30 minutes.
During his rest, he slips back 2 feet. How many hours will the monkey take to reach the top?
1) 15 2) 17 3) 19 4) 21

Question: A man covered a total distance of 1000 km in 16 hours, partly in a taxi at 36 km/hr and partly in
a bus at 80 km/hr. The distance covered by the bus is
A.892 Km B. Rs. 640 Km C. Rs. 720 Km D. None of these

Question: x, y and z are the three contestants in a kilometre race. If x can give y a start of 50 metres and x
can also give z a start of 69 metres, then how many metres start can y give to z, if the race is supposed to
end in a dead heat?
A. 19 metres B. 50 metres C. 59 metres D. 69 metres

Question: A train passes a 60 metres long platform in 20 seconds and passes a man standing on the
platform in 16 seconds. The speed of the train is
A. 54kmph B. 52kmph C. 45 kmph D. None of these

Question: Two trains starting from the same station and travelling in opposite directions are 227.5 km
apart in 3 hours 15 min. Had they been travelling in the same direction, they would have been 32.5 km
apart in the same time. Find their speeds (in kmph).
1. 30, 40 2. 20, 50 3. 35, 45 4. 10, 60

Question: The speeds of A and B are in the ratio 2 : 3. Starting from the same position, A takes 10 minutes
more than the time taken by B to reach a certain destination. If A had walked at double the speed, then he
would have covered the same distance in
(a) 10 minutes (b) 20 minutes (c) 25 minutes (d) 15 minutes

Question: A thief sees a policeman from 100 metres and runs off in the opposite direction at a speed of 15
km/hr. Two minutes later, the policeman sees the thief and chases him at a speed of 20 km/hr. How soon
will the policeman catch up with the thief?
1. 500 sec 2. 400 sec 3. 432 sec 4. 532 sec
Question: On a circular ground of 42 m diameter, Kenny and Gary start simultaneously from the same
starting point. Kenny runs back and forth along the diameter and Gary runs along the circumference, both
at a speed of 6 m/s. What will be distance between them after 22 seconds?
A. 36m B. 8m C. 34m D. 2m

Question: The ratio of downstream speed to upstream speed of a boat is 5 : 2. If the speed of the water in
the stream decreases by 1 km/hr, the ratio changes to 3 : 2. Find the speed of the boat in still water.
A. 35/4 km/hr B. 35/8 km/hr C. 5 km/hr D. None of these

Question: A boatman takes his boat upstream from place A to place B, where AB = 21 km. Then, he returns
to place A. He took 10 hours in total for the journey. If the time taken by him to go 7 km downstream is
equal to the time taken by him to go 3 km upstream, then find the speed of the river.
A. 2 km/hr B. 5 km/hr C. 3 km/hr D. 7 km/hr

Question: Two stations, Ahmedabad and Baroda, are 100 km apart. Navjeevan Express, travelling at 50
kmph, leaves Ahmedabad at 6:30 a.m. and Howrah-Ahmedabad Express, travelling at 40 kmph, leaves
Baroda at 7 a.m. At 7:30 a.m, Mr. Shah, the traffic controller, discovers that both the trains are travelling
on the same line. How much time is available for him to avert an accident?
A. 15 min B. 20 min C. 25 min D. 30 min

Question: Varun went for a long ride last Sunday. Every hour, he maintained a constant speed of 60 kmph.
But after every 1 hour ride, he took rest for 10 minutes. If he starts from a place A at 8 a.m. and reaches a
place B at 2 p.m. on the same day, what is the distance between A and B?
A. 250 km B. 300 km C. 310 km D. 360 km

Question: A train of length 500 m crosses a platform in 50 sec and another train of the same length,
moving in the opposite direction with double the speed of the first train, crosses the a pole in 20 sec. What
is the length of the platform?
A. 500 mt B. 250 mt C. 125 mt D. 625 mt

Question: Without stoppages, a train travels with an average speed of 40 km/hr, while with stoppages, it
covers the same distance with an average speed of 30 km/hr. What is the time (in minutes per hour) for
which the train stops?
A. 20 B. 30 C. 10 D. 15

Question: A father is chasing his son in their spacious backyard. His son, who is very agile on his feet, takes
8 leaps in the time taken by his father to take 5 leaps. However, father's leap is 4½ feet long, whereas the
son's leap is only 2½ feet long. How many leaps will father have to take before he catches his son, who was
10 feet away from him when the chase started?
(a) 22 leaps (b) 21 leaps (c) 20 leaps (d) 10 leaps

Question: Every day Neera’s husband meets her at the city railway station at 6.00 p.m. and drives her to
their residence. One day she left early from the office and reached the railway station at 5.00 p.m. She
started walking towards her home, met her husband coming from their residence on the way and they
reached home 10 minutes earlier than the usual time. For how long did she walk?
A. 1 hr B. 50 minutes C. 30 min D. 55 minutes

Question: The distance between two cities A and B is 1850 km. An Air India plane flies partly at 180 kmph
and partly at 190 kmph. Time taken to reach B from A is 10 hours. Also, it gives a better mileage of 3 km
per litre at 180 kmph than at 190 kmph. What volume of fuel does the plane consume when flying the
distance at 190 kmph if it consumes 48 litres while flying at 180 kmph?
A. 48.41 litres B. 60.32 litres C. 65.56 litres D. 86.2 litres

Question: A man standing inside a tunnel notices that Train A is running inside the tunnel with a speed of
45 kmph. Another Train B, which is half the length of Train A and coming from opposite direction, is
running at a speed of 81 kmph. Train A passes Train B in 4 seconds. Which of the following is the closest
approximation of the length of the tunnel, if Train A passes completely through it in 4 minutes?
(a) 3 km (b) 4 km (c) 5 km (d) 2 km

Question: Once a week, a wagon-driver leaves his hut and drives his wagon to the river dock to pick up
supplies for his town. At 4:05 p.m, one-fifth of the way to the dock, he passes a temple. At 4:15 pm, one-
third of the way, he passes Preetam-Da-Dhabaa. At what time will he reach the dock?
(a) 5:05 a.m (b) 5:05 p.m (c) 4:55 a.m (d) 4:55 p.m

Question: Two guns are fired from the same place at an interval of 12 minutes, but a person in a train
approaching the place hears the second shot 10 minutes after the first. Find the speed of the train if the
speed of sound is 330 m/s.
(a) 40 m/s (b) 46 m/s (c) 56 m/s (d) 66 m/s

Question: A soccer ball rolls at 4 m/s towards Marcos in a direct line from Michael. The ball is 15 m ahead
of Michael who is chasing it at 9 m/s. Marcos is 30 m away from the ball and is running towards it at 8 m/s.
The distance between Michael and Marcos when the ball is touched for the first time by one of them is
closest to _________.
1. 2 M 2. 2.25 M 3. 2.5 M 4. 2.75 M

Question: A ship develops a leak 12 km from the shore. Despite the leak, the ship is able to move towards
the shore at a speed of 8 km/hr. However, the ship can stay afloat only for 20 minutes. If a rescue vessel
were to leave from the shore towards the ship and it takes 4 minutes to evacuate the crew and passengers
of the ship, what should be the minimum speed of the rescue vessel in order to be able to successfully
rescue the people aboard the ship?
A. 53 km/hr B. 37 km/hr C. 28 km/hr D. Rs. 24 km/hr

Question: Saurav and Sachin are running on a 500 m circular track. Their speeds are 8 km/hr and 5 km/hr,
respectively. After what time will they meet for the first time at the starting point if they start
simultaneously in the same direction?
(a) 60 minutes (b) 45 minutes (c) 30 minutes (d) 20 minutes

Question: Towns P and Q are 100 km apart. A car leaves P at 12:00 noon and heads towards Q at a uniform
speed of 20 km/hr. There is a bus every half-an-hour from Q to P. If the bus service starts at 6 am and the
buses travel at a uniform speed of 25 km/hr, then how many buses will the car encounter between P and
Q?

Question: Shyam and Vyom walk up an escalator (moving stairway). The escalator moves at a constant
speed. Shyam takes three steps for every two steps of Vyom. Shyam gets to the top of the escalator after
taking 25 steps, while Vyom takes only 20 steps to reach the top. If the escalator was turned off, then how
many steps would they have to take to walk up to the top?
A. 40 B. 50 C. 60 D. 75

Question: A and B are running along a circular track in opposite directions. They meet at a point 450 m
from the starting point and continue running. They now meet again at a point 300 m from the starting
point, but in the opposite direction to before. What is the length of the track?

Question: Ravi, Manjit and Avtaar wanted to go out on a 200 km journey. In the beginning, Ravi and Manjit
went by scooter at a speed of 50 km/hr while Avtaar walked at a speed of 10 km/hr. After a certain
distance, Ravi got off and started walking at 10 km/hr, while Manjit took his scooter back to pick Avtaar
and arrived with him at the destination at the same time as Ravi. Find the total number of hours they took
to complete the journey?

Question: Kapil Dev and Bishan Singh Bedi started running at 8 am at the speeds of 40 km/hr and 18 km/hr,
respectively, towards Pragati Maidan from the India Gate. Bedi completed the whole distance with a
uniform speed. 1.5 hours after the start, Kapil Dev got stuck in traffic and reduced his speed. In the next 30
minutes, he could cover only 15 km and covered the remaining distance with a speed equal in magnitude
to the total time taken by Bedi in hours to cover the entire distance, and reached Pragati Maidan at the
same time as Bedi. At what time did both of them reach Pragati Maidan?
A. 1 AM B. 1 PM C. 11 PM D. Both (2) and (3)

Question: Mr. Racer started from Hyderabad to Bangalore with a speed of 60 kmph. After some time, he
changed his speed to 80 kmph and reached Bangalore. He returned with the same speed and changed his
speed to 60 kmph at the place where he had initially changed his speed in the onward journey, and came
back to Hyderabad. What was his average speed for the entire journey? (The distance between Hyderabad
and Bangalore is 600 km).

Question: A rat covers the distance directly as the square of the time taken to cover that distance. The
distance covered by one rat in 5 seconds is 4 m more than the other which runs for just 3 seconds with the
same speed. The time taken by a rat to cover the distance of 12 m is ___________.

(a) 4√3𝑠𝑒𝑐 (b) 2 sec (c) 3√3𝑠𝑒𝑐 (d) √3𝑠𝑒𝑐

Question: Two men are walking towards each other alongside a railway line. They both start at opposite
ends of a part of the railway track. One man is walking faster than the other. They pass each other 720
yards from the nearer of the two ends. When each man reaches the other end of the track, they stop for a
cigarette. Both men take exactly the same amount of time to smoke a cigarette. Then, they turn around
and head back to the original starting position. This time they meet 400 yards from the other end of the
track. What is the length of the track?
(a) 1760 yards (b) 2000 yards (c) 2160 yards (d) 2540 yards

Question: Two boats start at the same time from opposite sides of a river, travelling at right angles to the
shores at a constant speed. First time, they pass each other at a point 72 m from the nearer shore. Both
boats rest for 30 minutes at their respective shores before starting back. In the return trip, they meet at 40
m from the other shore. Find the width of the river.
(a) 170 m (b) 182 m (c) 196 m (d) 176 m

Question: In a 20 km long tunnel connecting two cities A and B, there are three gutters. The distance
between gutters 1 and 2 is half the distance between gutters 2 and 3. The distance from city A to its
nearest gutter - gutter 1 - is equal to the distance of city B from gutter 3. On a particular day, the hospital
in city A receives information that an accident has occurred at the third gutter. The victim can be saved
only if an operation is started within 40 minutes. An ambulance starts from city A at 30 km/hr and crosses
the first gutter after 5 minutes. If the driver doubles the speed after that, then what is the maximum
amount of time the doctor will get to attend the patient at the hospital before starting the operation.
Assume 1 minute elapses in taking the patient into and out of the ambulance.
A. 4 minutes B. 2.5 minutes C. 1.5 minutes D. The patient died before reaching the
hospital.
Question: A train approaches a tunnel AB. Inside the tunnel, a cat stands at a point which is equal 3/8 to of
the distance AB from the entrance A. When the train blows the horn, the cat starts to run. If the cat moves
towards the entrance A of the tunnel, the train will catch the cat exactly at the entrance. If the cat moves
towards the exit B, the train will catch the cat exactly at the exit. Find the ratio of the speed of train to that
of cat.
A. 3 : 1 B. 4 : 1 C. 5 : 1 D. 1 : 4