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

Directions: The problem contains a question and two statements giving certain data. You have to select the correct answer from the given options depending on the sufficiency of the data given in the statements to answer the question. Two trains T1 and T2 start respectively from P and Q towards each other simultaneously and meet at 11:30 a.m. What is the distance PQ, if Train T2 travels at a speed of 60 km/hr? (A) Train T1 leaves for Q at 9.30 a.m. at a speed of 40 km/hr. (B) The relative speed of the trains is 100 km/hr.

  1. Statement (A) alone is sufficient to answer the question and statement (B) alone is not sufficient to answer the question.

  2. Statement (B) alone is sufficient to answer the question and statement (A) alone is not sufficient to answer the question.

  3. Statements (A) and (B) together are sufficient to answer the question, but neither statement alone is sufficient.

  4. Each statement alone is sufficient to answer the question.

  5. Both statements (A) and (B) together are not sufficient to answer the question and additional data specific to the problem is needed.
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Directions: The following problem has a question and three statements labelled A, B and C. You have to determine which of the statements is/are sufficient to answer the question and then mark your answer accordingly. What is the time taken by Gaurav to reach home? A. If Gaurav increases his speed by 40%, it will take him 4 minutes less to reach home. B. If Gaurav decreases his speed by 30%, it will take him 6 minutes more to reach home. C. The speed of Gaurav is 10 km/hr.

  1. Only A is sufficient.

  2. Only B is sufficient.

  3. Only C is sufficient.

  4. Each of the statements A and B alone is sufficient.

  5. Each of the statements A, B and C alone is sufficient.
Reveal answer Fill a bubble to check yourself
D 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 give the answer. 1. If the data in statement I alone is sufficient to give the answer. 2. If the data in statement II alone is sufficient to give the answer. 3. If the data in statement I or statement II alone is sufficient to give the answer. 4. If the data in statement I and statement II together is not sufficient to give the answer. 5. If the data in statement I and statement II together is sufficient to give the answer. A motorcyclist travelled for 12 hours. What distance did he cover? I. He travelled half the distance at 30 km/hr and the other half at 40 km/hr. II. Had he travelled at 10 km/hr more, he would have saved 2 hours.

  1. (1)

  2. (2)

  3. (3)

  4. (4)

  5. (5)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I gives speeds for two halves, allowing calculation of average speed, but total distance cannot be found without time for each part. Statement II relates speed increase to time saved, which allows finding the original speed and distance. Both statements together are sufficient.

Multiple choice

Directions: In this 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. Atul covered a distance of 600 km, partly by train and partly by bus. What was the speed of the train? I. Total travelling time was 8 hours. II. Distance covered by bus was 120 km. III. If he had travelled 80 km more by bus, the journey time would have increased by 20 minutes.

  1. All statements together

  2. Only statement I

  3. Only statements I and II

  4. Only statements I and III

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

Let speed of train be T and bus be B. Distance = 600. I: T_time + B_time = 8. II: B_dist = 120, T_dist = 480. III: Relates change in time to change in distance. With all three, we have enough equations to solve for the variables.

Multiple choice

Two persons, Mohit and Sunny, are travelling by car towards each other at the same time from Jaipur Bus Stand and Delhi Bus Stand for their destinations Delhi Bus Stand and Jaipur Bus Stand, respectively. The distance between both bus stands is 300 km. Mohit meets Sunny 120 km away from Jaipur Bus Stand. A third person, Samir, starts from Jaipur Bus Stand to Delhi Bus Stand, 1 hour after Mohit starts. Samir meets Sunny 1.5 hour after he starts. If the speed of Samir is at least 20 km/h faster than the speed of Sunny, then which of the following statements is/are true? (a) The maximum possible speed of Sunny is 60 km/hr. (b) The minimum possible speed of Sunny is 60 km/hr. (c) The maximum possible speed of Mohit is 45 km/hr. (d) The minimum possible speed of Mohit is 45 km/hr.

  1. Only (a)

  2. Both (a) and (c)

  3. Both (b) and (d)

  4. Only (c)

  5. Only (b)
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

A boat takes (25 + N) hours for travelling downstream from point P to point Q and coming back to point R, which is M km from point Q. The distance between point P and point Q is D km. The boat takes 15 hours downward to cover distance from point P to point R, which is 75% of the distance from point P to point Q. The velocity of the stream is (4 - W) km/hr, the speed of the boat in still water is (14 + W) km/hr and the upstream speed of boat is 12 km/hr. Which of the following can be determined? A. Value of N B. Value of D C. Value of M D. Value of W

  1. All A, B, C and D

  2. Only B and C

  3. Only D and B

  4. Only A

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

The problem provides sufficient variables (N, D, M, W) and equations (downstream/upstream speeds, time taken, distances) to solve for all unknowns.

Multiple choice

Two cars X and Y start running at the same time respectively at the speeds of 20 km/hr and 5 km/hr in the opposite directions on the same road. Butterfly A sitting on the car X leaves the car and starts moving towards the car Y with the speed of 55 km/hr, touches the car Y and returns back to car X. This process is repeated till both the cars just cross each other. Initially, the distance between the two cars is 400 km. Find the distance travelled by the butterfly, if it starts at the same time as the two cars start running and doesn't take halts.

  1. 1180 km

  2. 880 km

  3. 1280 km

  4. 900 km

  5. 320 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The cars approach each other at a relative speed of 20 + 5 = 25 km/hr. The time taken for them to meet is 400 / 25 = 16 hours. Since the butterfly flies at a constant speed of 55 km/hr during this entire time, the total distance it covers is 55 * 16 = 880 km.

Multiple choice

Directions: In the following question, two quantities are given numbered I and II. Determine the relationship between the quantities and choose the appropriate option. Quantity I: The average speed (in kmph) over the distance, if a car covers four successive 20 km stretches at the speeds of 10 km/hr, 20 km/hr, 30 km/hr and 40 km/hr, respectively Quantity II: The average speed (in kmph) over the distance, if a bus travels the distances of 30 km, 80 km and 40 km at the speeds of 15 km/hr, 20 km/hr and 10 km/hr, respectively

  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 the relationship cannot be established from the information given.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Total distance = 80 km. Time = 20/10 + 20/20 + 20/30 + 20/40 = 2 + 1 + 2/3 + 1/2 = 3 + 4/6 + 3/6 = 3 + 7/6 = 25/6 hours. Average speed = 80 / (25/6) = 480/25 = 19.2 km/hr. Quantity II: Total distance = 30 + 80 + 40 = 150 km. Time = 30/15 + 80/20 + 40/10 = 2 + 4 + 4 = 10 hours. Average speed = 150/10 = 15 km/hr. Since 19.2 > 15, Quantity I > Quantity II.

Multiple choice

Directions: Read the following passage carefully and answer the question. Destinations A and B are 300 km apart from each other. Two persons P and Q start travelling towards each other from destinations A and B, respectively. They meet each other at a point O, which is 120 km away from destination A. Another person M starts travelling from destination A towards B. He has started his journey 1 hour after P started his journey. M meets Q 1.5 hours after he started his journey. If the speed of M is 20 km/hr faster than the speed of Q, at what speed should P travel so that he can meet Q and M at the same time?

  1. 45 km/hr

  2. 52.5 km/hr

  3. 65 km/hr

  4. 72.60 km/hr

  5. 76.40 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Directions: The following problem 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 give answer: (1) If the data in statement I alone is sufficient to answer the question (2) If the data in statement II alone is sufficient to answer the question (3) If the data in either statement I alone or statement II alone is sufficient to answer the question (4) If the data in statements I and II together is not sufficient to answer the question Two trains start from stations A and B and travel towards each other at the speeds of 50 km/hr and 60 km/hr, respectively. What is the distance between A and B? I. When they meet, the second train has travelled 120 km more than the first. II. They meet after 12 hours.

  1. (1)

  2. (2)

  3. (3)

  4. (4)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Relative speed is 50 + 60 = 110 km/hr. Statement I: Second train travels 120 km more than the first. In time t, 60t - 50t = 120, so 10t = 120, t = 12 hours. Distance = 110 * 12 = 1320 km. Statement II: They meet after 12 hours. Distance = 110 * 12 = 1320 km. Both statements independently give the answer.

Multiple choice

Directions: The question given below is followed by two statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. If Akshar and Arun left from Ludhiana at the same time, then what is the distance between Ludhiana and Delhi? I. Arun was travelling at an average speed of 60 kmph and reached Delhi at 6.00 p.m. II. Akshar reached Delhi at 8.00 p.m. and was travelling at an average speed of 40 kmph.

  1. The question can be answered by using statement I alone but cannot be answered by using statement II alone.

  2. The question can be answered by using statement II alone but cannot be answered by using statement I alone.

  3. Both statements I and II together are required to answer the question.

  4. The answer can be found by using any of the two statements alone.

  5. Both the statements together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Directions: The following problem consists of a question followed by three statements (A), (B) and (C). You have to determine which statement(s) is/are sufficient/necessary to answer the question. What would be the rate of flow of river? (A) The speed of a motorboat in still water is 4 km/hr. (B) It took 80 hours in total to travel downstream and then return after covering a distance of 70 km altogether. (C) Downstream speed > Speed of the motorboat in still water

  1. Only statement A is sufficient to answer the question.

  2. Both statements A and B are required to answer the question.

  3. Only statement B is sufficient to answer the question.

  4. None of the statements is sufficient to answer the question.

  5. All three statements together are sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Two trucks Truck-1 and Truck-2 go from factory to warehouse and vice versa. The distance from factory to warehouse is 100 km and there is only one straight road connecting them. One day, Truck-1 and Truck-2 start at the same time from factory and warehouse, respectively. Each of the trucks goes to its destination and then comes back, and repeats the process continually. Speeds of Truck-1 and Truck-2 are 30 km/hr and 70 km/hr. Where will Truck-1 and Truck-2 meet for the second time?

  1. 25 km from warehouse.

  2. 15 km from factory

  3. 25 km from factory

  4. 10 km from warehouse

  5. 20 km from factory
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Directions: In the question, two quantities are given, one as 'Quantity 1' and another as 'Quantity 2'. You have to determine relationship between the two quantities and choose the appropriate option. Quantity 1: The distance covered by a bus in 7 hours, if a car covered a distance of 1,500 km in 18.75 hours and the average speed of the bus is 17/16 of the average speed of the car. Quantity 2: The distance covered by a bike in 9.9 hours, if a person covered a distance of 16 km in 4 hours and the average speed of the bike is 1,500% of the average speed of the person.

  1. Quantity 1 > Quantity 2

  2. Quantity 1 ≥ Quantity 2

  3. Quantity 2 > Quantity 1

  4. Quantity 2 ≥ Quantity 1

  5. Quantity 1 = Quantity 2 or relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity 1: Car speed = 1500 / 18.75 = 80 km/h. Bus speed = (17/16) * 80 = 85 km/h. Distance = 85 * 7 = 595 km. Quantity 2: Person speed = 16 / 4 = 4 km/h. Bike speed = 1500% of 4 = 60 km/h. Distance = 60 * 9.9 = 594 km. Since 595 > 594, Quantity 1 > Quantity 2.