# CAT Practice : Speed Time, Races

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The following topics are covered in the CAT quant section from Arithmetic in Speed Time, Races. Detailed explanatory answers, solution videos and slide decks are also provided.
1. ### Speed Time - Races

Two friends A and B simultaneously start running around a circular track . They run in the same direction. A travels at 6 m/s and B runs at b m/s. If they cross each other at exactly two points on the circular track and b is a natural number less than 30, how many values can b take?

1. 3
2. 4
3. 7
4. 5
2. ### Speed Time - Geometry

Consider a square ABCD. EFGH is another square obtained by joining the midpoints of the sides of the square ABCD where E, F , G amd H are the midpoints of AB, BC, CD and DA respectively. Lakshman and Kanika start from points B and D respectively at speeds ‘l’ kmph and ‘k’ kmph respectively and travel towards each other along the sides of the square ABCD. Jagadeesh starts from Point E and travels along the Square EFGH in the anti-clockwise direction at ‘j’ kmph. Lakshman and Kanika meet for the second time at H where Jagadeesh also meets them for the first time. If l : k : j is 1: 3 : 5$\sqrt {2}$, then the distance travelled by Jagadeesh is

1. 7.5 × $\sqrt {2}$ times the side of the square ABCD
2. 7.5 × $\sqrt {2}$ times the side of the square EFGH
3. 7.5 times the side of the square ABCD
4. 7.5 times the side of the square EFGH
7.5 × $\sqrt {2}$ times the side of the square ABCD
• Polygons at top speed
• Hard
3. ### Speed Time - Cars

Three cars leave A for B in equal time intervals. They reach B simultaneously and then leave for Point C which is 240 km away from B. The first car arrives at C an hour after the second car. The third car, having reached C, immediately turns back and heads towards B. The first and the third car meet a point that is 80 km away from C. What is the difference between the speed of the first and the third car?

1. 60 kmph
2. 80 kmph
3. 20 kmph
4. 40 kmph
4. ### Speed Time - Cars

Three friends A, B and C decide to run around a circular track. They start at the same time and run in the same direction. A is the quickest and when A finishes a lap, it is seen that C is as much behind B as B is behind A. When A completes 3 laps, C is the exact same position on the circular track as B was when A finished 1 lap. Find the ratio of the speeds of A, B and C?

1. 5 : 4 : 2
2. 4 : 3 : 2
3. 5 : 4 : 3
4. 3 : 2 : 1
5. ### Speed Time

Mr. X decides to travel from Delhi to Gurgaon at a uniform speed and decides to reach Gurgaon after T hr. After 30 km, there is some engine malfunction and the speed of the car becomes ${ {4 \over 5} ^{th}}$ of the original speed. So, he travels the rest of the distance at a constant speed ${ {4 \over 5} ^{th}}$ of the original speed and reaches Gurgaon 45 minutes late. Had the same thing happened after he travelled 48 km, he would have reached only 36 minutes late. What is the distance between Delhi and Gurgaon?

1. 90 km
2. 120 km
3. 20 km
4. 40 km
6. ### Speed Time - Meeting point

Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds. They meet at a point in between the two cities and then proceed to their respective destinations in 54 minutes and 24 minutes respectively. How long did B take to cover the entire journey between City Q and City P?

1. 60
2. 36
3. 24
4. 48
7. ### Speed Time - Races

A swimming pool is of length 50 m. A and B enter a 300 m race starting simultaneously at one end of the pool at speeds of 3 m/s and 5 m/s. How many times will they meet while travelling in opposite directions before B completes the race?

1. Twice
2. Thrice
3. Once
4. 5 times
Thrice
• Racing on a swimming pool
• Medium
8. ### Relative Speed

Car A trails car B by 50 meters. Car B travels at 45km/hr. Car C travels from the opposite direction at 54km/hr. Car C is at a distance of 220 meters from Car B. If car A decides to overtake Car B before cars B and C cross each other, what is the minimum speed at which car A must travel?

1. 36 km/hr
2. 45 km/hr
3. 67.5 km/hr
4. 18 km/hr
67.5 km/hr
• Minimum overtaking speed
• Medium
9. ### Speed Time - Races

A and B stand at distinct points of a circular race track of length 120m. They run at speeds of a m/s and b m/s respectively. They meet for the first time 16 seconds after they start the race and for the second time 40 seconds from the time they start the race. Now, if B had started in the opposite direction to the one he had originally started, they would have meet for the first time after 40 seconds. If B is quicker than A, find B’s speed.

1. 3 m/s
2. 4 m/s
3. 5 m/s
4. 8 m/s
10. ### Boats and Streams

City A to City B is a downstream journey on a stream which flows at a speed of 5km/hr. Boats P and Q run a shuttle service between the two cities that are 300 kms apart. Boat P, which starts from City A has a still-water speed of 25km/hr, while boat Q, which starts from city B at the same time has a still-water speed of 15km/hr. When will the two boats meet for the first time? (this part is easy) When and where will they meet for the second time?

1. 7.5 hours and 15 hours
2. 7.5 hours and 18 hours
3. 8 hours and 18 hours
4. 7.5 hours and 20 hours
7.5 hours and 20 hours
• Downstream Upstream
• Medium
11. ### Relative Speed

Cities M and N are 600km apart. Bus A starts from city M towards N at 9AM and bus B starts from city N towards M at the same time. Bus A travels the first one-third of the distance at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmpr. Bus B travels the first one-third of the total time taken at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmph. When and where will the two buses cross each other?

1. 300 kms from A
2. 280 kms from A
3. 305 kms from A
4. 295 kms from A
295 kms from A
• Buses crossing
• Medium
12. ### Relative Speed

A car of length 4m wants to overtake a trailer truck of length 20m travelling at 36km/hr within 10 seconds. At what speed should the car travel?

1. 12 m/s
2. 14.8 m/s
3. 12.4 m/s
4. 7.6 m/s
13. ### Crossing and overtaking trains

Train A travelling at 63 kmph takes 27 to sec to cross Train B when travelling in opposite direction whereas it takes 162 seconds to overtake it when travelling in the same direction. If the length of train B is 500 meters, find the length of Train A.

1. 400 m
2. 810 m
3. 500 m
4. 310 m
310 m
• Crossing and overtaking trains
• Medium

P cycles at a speed of 4 m/s for the first 8 seconds, 5 m/s for the next 8 seconds, 6 m/s for the next 8 and so on. Q cycles at a constant speed of 6.5 m/s throughout. If P and Q had to cycle for a 400 m race, how much lead in terms of distance, can P give Q and still finish at the same time as Q?

1. 43.4 m
2. 56.6 m
3. 32.1 m
4. P cannot give a lead as Q is always ahead of P
15. ### Ratio of Speeds

A bus starts from a bus stop P and goes to another bus stop Q. In between P and Q, there is a bridge AB of certain length. A man is standing at a point C on the bridge such that AC:CB = 1:3. When the bus starts at P and if the man starts running towards A, he will meet the bus at A. But if he runs towards B, the bus will overtake him at B. Which of the following is true?

1. Bus travels 3x times faster than the man
2. Bus travels 2x times faster than the man
3. The bus and the man travel at the same speed
4. 4x the speed of the man is equal to 3x the speed of the bus
Bus travels 2x times faster than the man
• Ratio of Speeds
• Medium
16. ### Fuel Consumption

Ramesh takes 6.5 hours to go from city A to city B at 3 different speeds 30 kmph, 45 kmph, and 60 kmph covering the same distance with each speed. The respective mileages per liter of fuel are 11 km, 14 km and 18 km for the above speeds. Ramesh's friend Arun is an efficient driver and wants to minimise his friend's car's fuel consumption. So he decides to drive Ramesh's car one day from city A to city B. How much fuel will he be able to save?

1. 4.2 liters
2. 4.5 liters
3. 0.7 liters
4. 0.3 liters
4.5 liters
• Fuel Consumption
• Medium
17. ### Speed in a race

Amar, Akbar and Antony decide to have a 'x' m race. Antony completes the race 14 m ahead of Amar. Akbar finishes 20 m ahead of Antony and 32 m ahead of Amar. What is Amar’s speed?

1. 9/10th of Antony's speed
2. 5/8th of Akbar's speed
3. 14/15th of Antony's speed
4. 10/7th of Akbar's speed
9/10th of Antony's speed
• Speed in a race
• Medium
18. ### Distance between A and B

Tom, Jerry and Bill start from point A at the same time in their cars to go to B. Tom reaches point B first and turns back and meets Jerry at a distance of 9 miles from B. When Jerry reaches B, he too turns back and meets Bill at a distance of 7 miles from B. If 3 times the speed with which Tom drives his car is equal to 5 times Bill’s speed, what could be the distance between the points A and B

1. 40 miles
2. 24 miles
3. 31 miles
4. 63 miles
63 miles
• Distance between A and B
• Medium
19. ### Starting time

Kumar started from Chennai at x hrs y minutes and travelled to Vellore. He reached Vellore at y hrs z minutes. If the total travel time was z hrs and x minutes, his starting time in Chennai could have been ______ (Assume clock format to be 0 to 24 hrs).

1. 02:08 hrs
2. 13:03 hrs
3. 00:02 hrs
4. 12:01 hrs
20. ### Increasing Speed

When Sourav increases his speed from 20 Km/hr to 25 Km/hr, he takes one hour less than the usual time to cover a certain distance. What is the distance usually covered by him?

1. 125 Km
2. 100 Km
3. 80 Km
4. 120 Km
21. ### Increasing Speed

Distance between the office and the home of Alok is 100 Km. One day, he was late by an hour than the normal time to leave for the office, so he increased his speed by 5 Km/hr and reached office at the normal time. What is the changed speed of Alok?

1. 25 Km/hr
2. 20 Km/hr
3. 16 Km/hr
4. 50 Km/hr
22. ### Increasing Speed

Akash when going slower by by 15 Km/hr, reaches late by 45 hours. If he goes faster by 10 Km/hr from his original speed, he reaches early by by 20 hours than the original time. Find the distance he covers.

1. 8750 Km
2. 9750 Km
3. 1000 Km
4. 3750 Km
23. ### Increasing Speed

Raj was travelling to his hometown from Mumbai. He met with a small accident 80 Km away from Mumbai and continued the remaining journey at 4/5 of his original speed and reached his hometown 1 hour and 24 minutes late. If he had met with the accident 40 Km further, he would have been an hour late.
i) What is Raj's normal speed?
a) 20 Km/hr b) 15 Km/hr c) 30 Km/hr d) 25 Km/hr
ii) What is the distance between Mumbai and Raj's hometown?
a) 140 Km b) 200 Km c) 220 Km d) 250 Km

24. ### Distance betw A and B

Two persons A and B start moving at each other from point P and Q respectively which are 1400 Km apart. Speed of A is 50 Km/hr and that of B is 20 Km/hr. How far is A from Q when he meets B for the 22nd time?

1. 1000 Km
2. 400 Km
3. 800 Km
4. 1400 Km
25. ### Distance betw A and B

What would happen in the previous question if both A and B had started at point P.

1. 800 Km
2. 600 Km
3. 1000 Km
4. 350 Km
26. ### Trains A and B

Two trains A and B are 100 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.

1. 10 s
2. 6 s
3. 4 s
4. 8 s
27. ### Three Trains

Two trains start together from a Station A in the same direction. The second train can cover 1.25 times the distance of first train in the same time. Half an hour later, a third train starts from same station and in the same direction. It overtakes the second train exactly 90 minutes after it overtakes the first train. What is the speed of third train, if the speed of the first train is 40 Km/hr?

1. 20 Km/hr
2. 50 Km/hr
3. 60 Km/hr
4. 80 Km/hr
28. ### Relative Speed

Two trains left from two stations P and Q towards station Q and station P respectively. 3 hours after they met, they were 675 Km apart. First train arrived at its destination 16 hours after their meeting and the second train arrived at its destination 25 hours after their meeting. How long did it take the first train to make the whole trip?

1. 18h
2. 36h
3. 25h
4. 48h
29. ### Perpendicular Directions

Arjun travels from A to B, a distance of 200 Km at the speed of 40 Km/hr. At the same time, Rakesh starts from point C at a speed of 20 Km/hr along a roadwhich is perpendicular to AB. Find the time in which Arjun & Rakesh will be closer to each other?

1. 1.5 h
2. 3.33 h
3. 5 h
4. 4 h

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