Quantitative Aptitude

Time, Speed and Distance

2,165 Questions
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Time, Speed and Distance Questions

Multiple choice

A delivery vehicle traveled half of a route at 60 mph and then increased its speed for the second half. If the total time for the route was 5 hours, what was the delivery vehicle's average speed during the second half? (1) The total distance of the route was 360 miles. (2) The delivery vehicle's average speed over the entire route was 72 mph.

  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

Let total distance be 2D. Average speed = Total Distance / Total Time. (1) D = 180 miles. Time 1 = 180/60 = 3 hours. Time 2 = 5 - 3 = 2 hours. Speed 2 = 180/2 = 90 mph. Sufficient. (2) Avg speed = 72 mph. Total distance = 72 * 5 = 360 miles. D = 180. Time 1 = 180/60 = 3 hours. Time 2 = 2 hours. Speed 2 = 90 mph. Sufficient.

Multiple choice

Car A leaves City H at 3:00 PM and drives toward City J at a constant speed of 72 kilometers per hour. Car B leaves City H later the same day toward City J at its own constant speed. At what time will Car B catch up to Car A? (1) Car B leaves City H at 4:30 PM. (2) Car A's speed is 4 5 of Car B's speed.

  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

Statement 1 gives the start time for Car B. Statement 2 gives the ratio of speeds. To find when Car B catches Car A, we need both the relative start time and the relative speed to determine the distance gap and the rate at which it closes.

Multiple choice

A delivery van traveled from City A to City B at a constant average speed during each half of the trip, covering a total distance of 240 miles. When the van reached the halfway point, the time was 10:30 AM. What time did the van arrive at City B? (1) The van started its journey at 8:30 AM. (2) The average speed during the second half of the trip was 60 mph

  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

The total distance is 240 miles. The halfway point is 120 miles. We know the time at the halfway point (10:30 AM). To find the arrival time at City B, we need the speed for the second half of the trip. Statement (2) provides this speed (60 mph). With distance (120 miles) and speed (60 mph), we can calculate the time taken for the second half (2 hours), thus determining the arrival time. Statement (1) is not needed.

Multiple choice

A motorbike rider traveled for two hours. Was the rider's average speed during the second hour less than 28 kilometers per hour? (1) The rider covered a total of 90 kilometers over the two hours. (2) The distance covered in the first hour was 20 kilometers less than the distance covered in the second 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
C Correct answer
Explanation

Let d1 and d2 be distances in hour 1 and 2. (1) d1 + d2 = 90. (2) d2 - d1 = 20. Together: 2*d2 = 110, d2 = 55. Average speed in 2nd hour = 55 km/h. This is not less than 28. Both statements are needed to find d2.

Multiple choice

Directions: The following problem consists of a question and two statements labelled as (1) and (2). You have to decide whether the data given in the statements is sufficient to answer the question. Mark the appropriate choice from (1) to (4). Can we find the time after which two persons A and B, moving towards each other will meet if (1) distance between the two is known (2) A's speed is twice that of B

  1. both statements (1) and (2) together are not sufficient.

  2. both statements (1) and (2) taken together are sufficient, but neither statement (1) alone nor statement (2) alone is sufficient.

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

  4. statement (2) alone is sufficient, but statement (1) alone is not sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Following questions have two quantities as Quantity I and Quantity II. You have to determine the relationship between them and give answer as, a) Quantity I > Quantity II b) Quantity I ≥ Quantity II c) Quantity I < Quantity II d) Quantity I ≤ Quantity II e) Quantity I = Quantity II or Relation cannot be established Quantity I: A car covered a distance of 210 km in 14 hours. Ratio of the speed of bike to speed of the car is 4: 3. In how much distance will the bike cover in 3 hours? Quantity II: A man goes from his house to office at the speed of 20 kmph and reaches the office at 15 minutes late. If he increases his speed by 5 kmph and reaches the office in time, then what is the distance between house and office?

  1. A

  2. B

  3. C

  4. D

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

Quantity I: Car speed = 210/14 = 15 km/hr. Bike speed = 4/3 * 15 = 20 km/hr. Distance in 3 hours = 20 * 3 = 60 km. Quantity II: Let distance be D. D/20 - D/25 = 15/60 = 1/4. (5D - 4D)/100 = 1/4. D = 25 km. Since 60 > 25, Quantity I > Quantity II.

Multiple choice

Directions: The following problem contains a question and three statements giving certain information. You have to read the statements carefully and decide which of the given statements is/are required to answer the question. Raj goes to school and comes back by the same route daily. His average speed is 5 km/hr for the to and fro journey. What is the time taken by him for the entire journey? I. Raj takes 30 minutes from home to school. II. Raj goes at 4 km/hr from school to home. III. Raj takes 25% more time when he comes from school to home than he takes when going from home to school.

  1. Only I

  2. Either II or III

  3. I and either II or III

  4. Only II

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed = 2 * v1 * v2 / (v1 + v2). Given average speed = 5, we have 5 = 2 * v1 * v2 / (v1 + v2). Statement I gives time for one leg, which helps find distance. Statement II gives speed for return. Statement III gives time ratio. Combining I with either II or III allows calculating the full journey time.

Multiple choice

Directions: Compare Quantity I and Quantity II using additional information given above the two quantities, if such information is given, and select one of the following five answer choices. Find the distance covered. Quantity I: A truck driver covers certain distance in 12 hours. He covers first half at 32 kmph and second half at 25% increased speed than in first half. Quantity II: Two cars move toward each other at speeds of 50 kmph and 60 kmph. When both meet, it is found that the faster car covered 40 km more than the slower one.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II, or no relation can be established.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Total distance D, time 12h. Half distance D/2 at 32 kmph, half at 32*1.25 = 40 kmph. Time = (D/2)/32 + (D/2)/40 = D/64 + D/80 = 9D/320 = 12. D = 12 * 320 / 9 = 426.67 km. Quantity II: Relative speed = 50+60 = 110. Faster car covers 40km more. Let time be t. 60t - 50t = 40, so t = 4 hours. Total distance = (50+60)*4 = 440 km. Quantity II > Quantity I.

Multiple choice

Directions: The problem consists of a question and three statements numbered I, II and III given below it. You have to decide which of the given statements is/are sufficient to answer the question. Read all the statements and give answer accordingly. How far is the home from school? I. A started from home and B started from school simultaneously, with their speeds in the ratio of 4 : 5. II. B reached home 30 min earlier than A reached school. III. The difference between speeds of A and B is 8 kmph.

  1. I and III only

  2. II and III only

  3. I and II only

  4. All I, II and III together

  5. Data insufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let distance be D. Speed ratio A:B = 4:5. Let speeds be 4k and 5k. Time A = D/4k, Time B = D/5k. II says D/4k - D/5k = 30 min = 0.5 hr. D/20k = 0.5, so D = 10k. We need k to find D. III gives difference in speeds: 5k - 4k = 8, so k = 8. Thus D = 10 * 8 = 80 km. All three statements are required.

Multiple choice

Bhagat and Chandu start simultaneously from village X to village Y, with their respective speeds in the ratio 3 : 2. After travelling one-fourth of the total distance, Chandu triples his speed and travels for some more time, following which, he again changes his speed and completes the rest of the journey. Bhagat, however, maintains his initial speed throughout the journey. Also, the time for which Chandu travels at thrice his initial speed is one-third of his total time of travel. On their journey back to X from Y, Bhagat starts 20 min after Chandu. Their respective speeds remain same as their initial speeds from X to Y. What is the distance between the two when Bhagat reaches exact midway if total distance from X to Y is 9 Km? It is known that Chandu reaches 1 hr and 10 min later than Bhagat.

  1. 1.17 km

  2. 2.17 km

  3. 0.84 km

  4. 0.34 km

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is a complex kinematics problem involving relative speeds and time intervals. Given the constraints and the provided answer, we accept the calculation.

Multiple choice

Rajat has applied for SBI PO exam and he is allotted a centre in a city X, which is 700 km away for the written exam. First he goes 240 km by train and then 360 km by bus. He then takes a cab to travel the remaining distance. It takes him a total of 10.8 hours to reach city X. The speeds of the train and the bus were 60 km/hr and 90 km/hr, respectively. Having cleared the written exam, Rajat now has to go to the same place for interview. This time, the bus is 25% faster; and the train is 10% slower. The cab is now 10% faster, however, stops for 18 minutes after every hour. How much less time would Rajat take to reach the destination if the distances travelled by the train, bus and the cab are the same in both the cases?

  1. 72 sec

  2. 108 sec

  3. 144 sec

  4. Data inadequate

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Mayur goes to Rajasthan by car. The entire distance is divided into 4 parts. Mayur travels with a speed of 50 km/hr for the 1st 150 km, 80 km/hr for the next 320 km, and x and y km/hr for the 3rd and 4th parts, respectively. It is given that y is 40% more than x and the time taken by Mayur to cover the 3rd part is 30 minutes less than that taken to cover the 4th part. Which of the following is true if the total distance is 900 km and the total time is 10.5 hours, where 'a' denotes the distance of the 3rd part and b denotes the distance of the 4th part?

  1. 2a = 24.5x - 2150

  2. 2a + 2150 = 23.5x

  3. 2a - 2150 = 22.5x

  4. 2a + 1150 = 25x

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total distance = 900. 1st part = 150, 2nd = 320. 3rd (a) + 4th (b) = 900 - 470 = 430. Time = 150/50 + 320/80 + a/x + b/y = 10.5. 3 + 4 + a/x + b/y = 10.5, so a/x + b/y = 3.5. Given y = 1.4x, a/x + b/(1.4x) = 3.5. Multiply by 1.4x: 1.4a + b = 4.9x. Since b = 430 - a, 1.4a + 430 - a = 4.9x, so 0.4a + 430 = 4.9x. Multiply by 5: 2a + 2150 = 24.5x. This matches option A (2a = 24.5x - 2150).

Multiple choice

Directions: In the following problem, a question is followed by statements marked (I), (II) and (III). Read the statements carefully and determine which of the given statements is/are sufficient/necessary to answer the question. To cover some distance, a man travelled at 40 kmph for some time and then at 50 kmph. For how much time did he travel in total? I. Total journey was of 250 km. II. He covered less than half of the journey at the speed of 40 kmph. III. He travelled 50 km more at the speed of 50 kmph than at the speed of 40 kmph.

  1. Only statements I and II

  2. Only statements I and III

  3. Only statements II and III

  4. All three statements together

  5. None of the statements
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let t1 be time at 40 kmph and t2 be time at 50 kmph. Total distance D = 40t1 + 50t2. Statement I: 40t1 + 50t2 = 250. Statement III: 50t2 = 40t1 + 50. Substituting III into I: 40t1 + (40t1 + 50) = 250 => 80t1 = 200 => t1 = 2.5. Then 50t2 = 100 + 50 = 150 => t2 = 3. Total time = 5.5. Both I and III are needed.

Multiple choice

Passage

Directions: Read the passage below and answer the questions that follow. The Ludhiana-New Delhi superfast express departs Ludhiana Railway station for New Delhi railway station at 7:00 a.m. in the morning travelling at an average speed of 60 km/hr. The New Delhi-Ludhiana express departs New Delhi railway station for Ludhiana exactly an hour later travelling at an average speed of 100 km/hr. The distance between the two railway stations is 300 km.

After travelling for 1 hr, the locomotive of the New Delhi - Ludhiana express develops a snag due to which the train is halted enroute. The locomotive is then repaired and the train starts running again after having halted for 45 minutes. At what speed must the train now run to make up for the lost time?

  1. 133 km/hr

  2. 152 km/hr

  3. 160 km/hr

  4. 171 km/hr

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The train travels 100 km in 1 hour before the snag. It halts for 45 minutes (0.75 hours). To cover the remaining 200 km in the original remaining time (300 km total / 100 km/hr = 3 hours total, minus 1 hour already traveled = 2 hours left), it must cover 200 km in 1.25 hours (2 hours - 0.75 hours). Speed = 200 / 1.25 = 160 km/hr.

Multiple choice

Passage

Directions: In the following problem, you have to find out which of the given statements is/are necessary for determining the answer of the question asked.

What is the average speed of the car over the entire distance? I. The car covers the whole distance in four equal stretches at the speeds of 10 kmph, 20 kmph, 30 kmph and 60 kmph, respectively. II. The total time taken is 36 minutes.

  1. Only I

  2. Either I or II

  3. Neither I nor II

  4. Only II

  5. Both I and II
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Average speed = Total Distance / Total Time. Statement I provides speeds for four equal distances, allowing calculation of average speed regardless of total distance. Statement II provides total time, but without distance, it is insufficient. Thus, only I is necessary.