Quantitative Aptitude

Time, Speed and Distance

2,165 Questions
All Core formulas and unit conversion 441 Boats and streams effective speed 396 Relative speed, meetings, and overtaking 375 Average speed 362 Early and late arrival 321 Proportional relationships 202 Stoppage time per hour 35 Train and stationary or moving object crossing 17 Races and dead heats 16

Time, Speed and Distance Questions

Multiple choice

In the given questions, two quantities are given, one as Quantity I and another as Quantity II. You have to determine relationship between two quantities and choose the appropriate option Two buses A and B starts to move each other from P and Q. Distance between P and Q is 280 km. Max speed of Bus A and Bus B is 40 km/hr and 30 km/hr Quantity I: Time taken by the bus to cross each other Quantity II: Time taken by Car 'Z' to cover 160 km distance at a speed of 40km/hr.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or No relation
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Directions: The question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and mark the correct answer. A car travels along a path A-B-C-D (along segments AB, BC and CD). Points A, B, C, D are equidistant from each other, what was the speed of the car while travelling in the segment CD? I. The total distance covered by the car is 288 km and the speed of the car in segment BC is 72 km/h. II. The average speed of the car during the entire journey is 74 km/h. The speed of the car to cover segments AB, BC and CD is in the ratio of 15 : 12 : 10, respectively.

  1. The data in both the statements I and II together is necessary to answer the question.

  2. The data either in statement I alone or in statement II alone is sufficient to answer the question.

  3. The data in both the statements I and II together is not sufficient to answer the question.

  4. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  5. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Amtrak train covers a certain distance from Quebec to Alabama in 3 hours at a certain speed. What would be the speed to cover the same distance in 2 hours? (1) Speed of the train to cover the same distance in 3 hours is more than 50 miles per hour. (2) The difference in speed of the train when covering the distance in the stated durations is 30 miles per hour.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let d be the distance and v be the speed. We know d/3 = v. We want to find the speed v' = d/2. Statement 1 gives v > 50, which is not enough to find v'. Statement 2 gives v' - v = 30. Since v' = 1.5v, we have 1.5v - v = 30, so 0.5v = 30, v = 60. Thus, v' = 90. Statement 2 is sufficient.

Multiple choice

Will Peter reach his office on time, if he leaves home at 8 am and his office is at a distance of 8 miles from his home, and his office timings start at 8:15 am? (1) He travels the first 5 miles at a speed of 30 miles per hour and the rest at a speed of 20 miles per hour. (2) He travels at a speed of 20 miles per hour for the first 5 minutes and then increases his speed by 60%.

  1. Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement 1: Total time = 5/30 + 3/20 = 1/6 + 3/20 = 10/60 + 9/60 = 19/60 hours = 19 minutes. He arrives at 8:19, so he is late. Statement 2: 5 mins at 20 mph = 5/60 * 20 = 5/3 miles. Remaining 6.33 miles at 32 mph takes ~12 mins. Total time is 17 mins, he is late. Both are sufficient to determine he is late.

Multiple choice

Directions: Compare the two quantities in A and B. When Pat drives from his home to the nearest mountain resort, it takes 5 hours at an average speed of 50 miles per hour. When Fred drives from his home to his beach house, it takes 3.2 hours at an average speed of 60 miles per hour. Quantity A Quantity B Pats driving distance from his home to the nearest mountain resort. Freds driving distance from his home to his beach house.

  1. Quantity A is greater than quantity B.

  2. Quantity B is greater than quantity A.

  3. Both quantities are equal.

  4. The relationship between the quantities cannot be determined.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity A: 5 hours * 50 mph = 250 miles. Quantity B: 3.2 hours * 60 mph = 192 miles. 250 > 192.

Multiple choice

A fighter plane traveling at u km/hr wants to refuel itself in mid-air. It sights a refueling station coming towards it with a speed of v km/hr. The angle of elevation from the refueling station and the shortest distance between them are 30° and 220Km respectively. The plane sends a signal for refueling to the refueling station. It receives a confirmation in 10 minutes. During this time, the angle of elevation changes to 60°. If the vertical distance between them remains the same throughout and u:v=10:1, find the speed of the refueling station.

  1. 40 km/hr

  2. 40 √3 km/hr

  3. 45 km/hr

  4. 45 √3 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Baron drove from his house to his cousin's house and then drove back from there to his house. He took two different routes, one for going and one for coming. While driving from his house to his cousin's house, he drove at a speed of 36 mph, and while returning from his cousin's house to his house, his speed was 48 mph. What was his average speed for the total distance? (1) The distance of the first route was 24% of the entire distance he travelled. (2) The distance of the second route was 100 miles.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Average speed = Total distance / Total time. Let d1 and d2 be distances. Total time = d1/36 + d2/48. Statement 1 gives d1 = 0.24 * (d1+d2), which allows expressing d1 in terms of d2. This is sufficient to calculate the average speed.

Multiple choice

What is the distance between Harry's home and his office? (1) Harry's average speed on his commute to work this Monday was 30 miles per hour. (2) If Harry's average speed on his commute to work this Monday had been twice as fast, his trip would have been 15 minutes shorter.

  1. Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.

  2. Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are not sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let d be distance, v be speed, t be time. (1) v = 30. We have d = 30t. Two variables, not sufficient. (2) If speed is 2v, time is t - 15/60. d = 2v(t - 0.25). We have two equations: d = vt and d = 2v(t - 0.25). Substituting v = 30, we get d = 30t and d = 60(t - 0.25). 30t = 60t - 15 => 30t = 15 => t = 0.5. Then d = 15. Both statements are needed.

Multiple choice

Two brothers, David and Joseph, started traveling to their aunt Sophia's town. Both decided to go separately using different means of transportation. David decided to travel through a train and Joseph through a car. The speed of the train was 50% more than that of the car. Joseph and David both first arrived at the railway station. David then moved to his train. Then, both started from there together at the same time and reached their aunt's place, which was 75 miles away, at the same time. On the way, the train lost 15 minutes while stopping at stations. What was the speed of the car?

  1. 125 miles per hour

  2. 120 miles per hour

  3. 110 miles per hour

  4. 100 miles per hour

  5. 95 miles per hour
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let car speed be v. Train speed = 1.5v. Time for car = 75/v. Time for train = 75/(1.5v) + 15/60 = 50/v + 0.25. Since they arrive together: 75/v = 50/v + 0.25 -> 25/v = 0.25 -> v = 100.

Multiple choice

Directions : Answer the questions independently of each other. Well trodden paths connecting points A, B and C form a right-angled isosceles triangle with A and C being equidistant from B. Ravi decides to travel from point A to point C using the shortest path. Exactly halfway through the journeyhe meets with an accident and has to be rushed to the hospital located at point B. On path AB, the maximum speed the vehicle can travel at is 40 km/hr, on path BC it is 60 km/hr and on path CA it is 60√2 km/hr. There is also an untrodden path from the accident spot to the hospital at point B (which is also the shortest possible route between the two points). The maximum speed with which a vehicle can travel on any untrodden path is 30√2 km/hr. The distance between A and B is 2 km. What is the difference in time taken between the fastest two routes to reach the hospital? (Assume vehicles can travel only on the routes mentioned above).

  1. 1 min

  2. 20 min

  3. 1 hour

  4. 2 hours

  5. 5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The triangle is right-angled isosceles with AB = BC = 2 km and AC = 2*sqrt(2) km. The shortest path from A to C is the hypotenuse (2*sqrt(2) km). Halfway is sqrt(2) km. The accident spot is on the hypotenuse. The distance from the accident spot to B is 1 km. Calculating the time for the two fastest routes yields a difference of 1 minute.

Multiple choice

How much time does Mr. Richards take to reach his office from home? (1) One day, he started 30 minutes late from home and reached his office 50 minutes late, while driving 25% slower than his regular speed (2) He needs to drive at a constant speed of 25 miles per hour to reach his office just in time if he is 30 minutes late from home.

  1. if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient;

  2. if statement (2) ALONE is sufficient to answer the question but statement (1) alone is not sufficient.

  3. if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient;

  4. if EACH statement ALONE is sufficient to answer the question;

  5. if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement (1) allows us to set up equations for regular speed and time. Let T be regular time and S be regular speed. D = S*T. New scenario: D = 0.75S * (T + 50/60). Since D is constant, S*T = 0.75S * (T + 5/6). This allows solving for T. Statement (2) is also sufficient but (1) alone is sufficient.

Multiple choice

Statement 1: A car travels a distance of 60 km at a constant speed of 40 km/h. It then travels another 60 km at a constant speed of 60 km/h. The average speed of the car for the entire journey is 48 km/h. Statement 2: A ball is thrown from the top of a building and reaches a maximum height of 20 metres. The time taken by the ball to reach the maximum height is half the time taken to reach the ground. In the light of the above statements, choose the most appropriate answer from the options given below:

  1. Both statement 1 and statement 2 are correct.

  2. Both statement 1 and statement 2 are incorrect.

  3. Statement 1 is correct, but statement 2 is incorrect.

  4. Statement 1 is incorrect, but statement 2 is correct.
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

The following problem consists of a question and two statements numbered 1 and 2. You have to decide whether the data provided in the statements is sufficient to answer the question. Rahim is riding upstream on a boat, from point A to B, at a constant speed. The distance from A to B is 30 km. One minute after Rahim leaves from point A, a speedboat starts from point A to go to point B. It crosses Rahim's boat after 4 minutes. If the speed of the speedboat is constant from A to B, what is Rahim's speed in still water? 1. The speed of the speedboat in still water is 30 km/hour. 2. Rahim takes three hours to reach point B from point A.

  1. Statement 1 alone is sufficient to answer the question, but statement 2 alone is not sufficient.

  2. Statement 2 alone is sufficient to answer the question, but statement 1 alone is not sufficient.

  3. Each statement alone is sufficient.

  4. Both statements together are sufficient, but neither of them alone is sufficient.

  5. Statements 1 & 2 together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Directions: In this problem, a question is given followed by three statements numbered I, II and III. Read the statements carefully and decide which of them is/are sufficient/required to answer the question. What is the time taken by Lisa to complete a 10-kilometre race? Statements: A. If Lisa increases her speed by 20%, she will finish the race 5 minutes earlier. B. If Lisa decreases her speed by 15%, she will finish the race 6 minutes later. C. Lisa's speed is 8 km/hr.

  1. Only C is sufficient.

  2. Only B and C are sufficient.

  3. Only A and C are sufficient.

  4. Each of the statements A, B and C alone is sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let speed be v and time be t. Distance = 10. v*t = 10. Statement A: 1.2v * (t - 5/60) = 10. Statement B: 0.85v * (t + 6/60) = 10. Statement C: v = 8. Each statement provides enough info to solve for t.

Multiple choice

Directions: The following question is accompanied by statements 1 and 2. You have to determine which of the following statements(s) is/are sufficient/necessary to answer the question. A car and a motorcycle start simultaneously from points P and Q, respectively, and travel towards each other. The distance between P and Q is 520 kilometres. Find the time taken by motorcycle to reach point P. Statement 1: The speeds of the car and the motorcycle are in the ratio 5 : 3. Statement 2: The car and the motorcycle meet each other after 5 hours.

  1. Statement 1 alone is sufficient.

  2. Statement 2 alone is sufficient.

  3. Both statements together are sufficient, but neither statement alone is sufficient.

  4. Each statement alone is sufficient.

  5. Statements 1 and 2 together are not sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speeds be 5v and 3v. Total distance = 520. Time = 5 hours. 5v*5 + 3v*5 = 520 => 40v = 520 => v = 13. Speed of motorcycle = 3*13 = 39 km/h. Time to reach P = 520 / 39. Both statements are required to find the speed and the time.