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

A man travels 15 km at a speed of 30 kmph, 50 km at a speed of 20 kmph and 30 km at a speed of 120 kmph. Find the time taken throughout the journey.

  1. 3.25 hours

  2. 3 hours

  3. 2.5 hours

  4. 2 hours
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The total time taken is the sum of the times for each segment of the journey. The first segment takes 15/30 = 0.5 hours, the second takes 50/20 = 2.5 hours, and the third takes 30/120 = 0.25 hours. Adding these together gives a total journey time of 3.25 hours.

Multiple choice

The speeds of two buses, Bus P and Bus Q, are p km/h and q km/h, respectively, where p > q. The speeds p and q are the roots of the equation x2 - 144x + 5,120 = 0. Let TP and TQ be the usual times taken by Bus P and Bus Q, respectively, to cover a certain distance D km. If their speeds are interchanged for the same distance D, Bus P takes (TP + 3) hours and Bus Q takes (TQ - 3) hours. Find TP + TQ.

  1. 24 hours

  2. 25 hours

  3. 26 hours

  4. 27 hours

  5. 28 hours
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Roots p, q of x^2 - 144x + 5120 = 0. p+q = 144, pq = 5120. Solving gives 80 and 64. D/q - D/p = 3 and D/p - D/q = -3. Using D/64 - D/80 = 3 => (5D-4D)/320 = 3 => D = 960. T_P = 960/80 = 12, T_Q = 960/64 = 15. T_P + T_Q = 12 + 15 = 27.

Multiple choice

Each of the questions 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 are sufficient to answer the question. Read both the statements and give answer-(1) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question. (2) If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question. (3) If either of the data in statement I alone or in statement II alone are sufficient to answer the question. (4) If the data in both statements I and II together are not sufficient to answer the question. (5) If the data in both the statement I and II together are necessary to answer the question. What is the speed of the train? I. The train covers a distance of 215 km in 5 hours. II. The train covers a distance of 370 km in 8 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: Speed = 215/5 = 43 km/hr. Statement II: Speed = 370/8 = 46.25 km/hr. Either statement alone is sufficient to find the speed.

Multiple choice

Directions: The following question is accompanied by statements A, B and C. You have to determine which of the statements is/are sufficient/necessary to answer the question. Anupam and Brewster are chasing each other. What is the distance between them after 9 minutes? A. Brewster is followed by Anupam at a distance of 1300 m. B. Anupam and Brewster start running at the rates of 13 km/hr and 19km/hr, respectively. C. The relative speed of Anupam and Brewster is 6 km/hr.

  1. C alone is sufficient.

  2. Only B and C are sufficient.

  3. A and C together are sufficient.

  4. All together are necessary.

  5. Either B or C is sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the distance after 9 minutes, we need the initial distance (A) and the relative speed (C). Statement B is redundant if C is provided.

Multiple choice

Directions: The following question is accompanied by statements A, B and C. You have to determine which of the statements is/are sufficient/necessary to answer the question. What is the ratio between the speed of water current and that of Ameera's boat, respectively? A. Ameera's boat running upstream takes 7 hours 38 minutes to cover a certain distance. B. It takes 2 hours to cover the same distance running downstream. C. There is one more boat travelling upstream at a speed of 21 km/hr.

  1. A and B together are sufficient.

  2. Only B is sufficient.

  3. Only A and C are sufficient.

  4. B and C are sufficient.

  5. All of them are necessary.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let boat speed be B and current speed be C. Statement A gives B-C. Statement B gives B+C. With both, we have a system of two equations with two variables, allowing us to solve for B and C and thus their ratio. Statement C is irrelevant as it describes a different boat.

Multiple choice

Directions: The following problem consists of a question followed by two statements. Read the statements carefully and decide which of them is/are sufficient/necessary to answer the question. A man walks from his house at a speed of 9 km/hr and reaches his office 10 minutes late. Find the distance of the office from his house. I. If his speed had been 12 km/hr, he would have reached 20 minutes early. II. He walked in south direction and a man crossed him walking at a speed of 6 km/hr.

  1. Only statement II is sufficient.

  2. Both statements are necessary.

  3. Only statement I is sufficient.

  4. Neither statement I nor statement II is sufficient.

  5. Either statement I or statement II is sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let d be distance, t be time. d/9 = t + 1/6 (10 mins late). d/12 = t - 1/3 (20 mins early). Subtracting: d/9 - d/12 = 1/6 + 1/3 = 1/2. d/36 = 1/2, d = 18 km. Statement I is sufficient. Statement II is irrelevant.

Multiple choice

Directions: Each of the questions 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 are sufficient to answer the question. Read both the statements and give answer: Prem and Ramesh started from two cities Patna and Allahabad respectively, traveling at constant speeds, to reach Allahabad and Patna respectively. At what time will they meet? Statement I: The distance between Patna and Allahabad is 250 km. Prem travels at 50 km/hr and Ramesh travels at 25 km/hr Statement II: Prem started from Patna at 5:00 a.m. and reached Allahabad at 11:00 a.m. Ramesh started from Allahabad at 7:00 a.m. and reached Patna at 3.00 p.m.

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

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

  3. The data in statements I alone or in statement II alone is sufficient to answer the question.

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

  5. The data in both the statements I and II together is necessary to answer the question.
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question. A boat starts from point A at 7:00 a.m. for point B. Find the distance between points A and B. Statement I: The ratio of the downstream speed to speed of the boat is 4:3 respectively. The difference between the time taken for going from point A to point B and that of the same while returning is 1 hour. Statement II: The boat reached point B at 11:00 a.m. Statement III: The speed of stream is 2 km/h.

  1. The data in statement I and statement II together are necessary to answer the question, while data in statement III alone is not sufficient to answer the question.

  2. The data in statement I and statement III together are necessary to answer the question, while data in statement II alone is not sufficient to answer the question.

  3. The data in statement II and statement III together is necessary to answer the question, while data in statement I alone is not sufficient to answer the question.

  4. Either option (a) or option (c)

  5. All the statements together are necessary to answer the question.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I gives the ratio of downstream speed to boat speed, but not the actual speeds. Statement II gives the time duration (4 hours). Statement III gives the stream speed. With stream speed and the ratio from I, we can find the boat speed. With boat speed and time from II, we can find distance. Thus, I and III are needed to find the boat speed, and II is needed to find the distance.

Multiple choice

Each of the questions below, consist a question and two statements numbered I and II. You have to decide whether the data provided in the statements are sufficient to answer the question. Read the two statements and Give answer Train departs at 8 pm. At what time will it reach its destination? Statements: I. Distance is 200 km. and speed is 40 km/h. II. It reaches before 11 pm but after 10 pm.

  1. If the data in statement I and II together are sufficient to answer the question

  2. If the data in statement I and II together are not sufficient to answer the question

  3. If the data in statement II alone sufficient to answer the question, while the data in statement I are not required to answer the question.

  4. If the data in statement I alone sufficient to answer the question, while the data in statement II are not required to answer the question.

  5. Either data in statement I or II is alone sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives distance (200 km) and speed (40 km/h), so time taken = 200/40 = 5 hours. Departing at 8 pm, the train reaches at 1 am. Statement I is sufficient alone.

Multiple choice

Each of the questions 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 are sufficient to answer the question. Read both the statements and give answer: One day I left my home at 7 : 00 AM and assumed that if I run at uniform speed then I will reach my school at 12 : 00 AM. If my brother left the school for home at 8 : 00 AM with his uniform speed then at what time will he meet me? Statement I : The uniform speed of my brother is 14 km per hour. Statement II : He can reach home at 11:30 AM.

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

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

  3. Either Statement I or Statement II alone is sufficient to answer the question.

  4. Neither statement I nor statement II is sufficient to answer the questions.

  5. The data in both the statements I and II together is necessary to answer the question
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement II gives the brother's travel time from 8:00 AM to 11:30 AM, which determines his speed relative to the known journey. This is enough to calculate where the two travelers meet. Statement I gives only his speed, without the distance or the first traveler's speed, so it is insufficient alone.

Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. (only quantity is to be considered) Quantity I : The ratio of speed of stream and speed of a boat is 1 : 3 respectively. If the boat can cover 420 km while travelling downstream in 7 hours, then how long would it take to cover 270 km while travelling upstream? Quantity II : Boat M can travel 400 km upstream and then 400 km downstream in total time of 18 hours. If the speed of the boat is 45 km/hr, then how long would it take boat M to only travel downstream 400 km?

  1. Quantity : I > Quantity : II

  2. Quantity : I ≥ Quantity : II

  3. Quantity : I < Quantity : II

  4. Quantity : II ≥ Quantity : I

  5. Quantity I = Quantity II or relation can't be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For Quantity I: Downstream speed = 420/7 = 60 km/hr. Ratio of stream to boat is 1:3, so stream=15, boat=45. Upstream speed = 45-15 = 30 km/hr. Time = 270/30 = 9 hours. For Quantity II: Let boat speed = 45, stream = s. 400/(45-s) + 400/(45+s) = 18. Solving gives s=5. Downstream time = 400/(45+5) = 8 hours. Since 9 > 8, Quantity I > Quantity II.

Multiple choice

The question is followed by two statements, I and II. Mark the answer as per the given conditions. [CAT 1991] A train started from Station A, developed engine trouble and reached Station B, 40 minutes late. What is the distance between Stations A and B? I. The engine trouble developed after travelling 40 km from Station A and the speed reduced to (1/4)th of the original speed. II. The engine trouble developed after travelling 40 km from station A in two hours and the speed reduced to (1/4)th of the original speed.

  1. statement I alone is required to answer the question, but not statement II.

  2. statement II alone is required to answer the question, but not statement I.

  3. both statements I and II together are needed to answer the question.

  4. can be answered by both statements independently.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I provides the distance and speed ratio but not the time taken to travel the first 40 km. Statement II specifies the time taken (2 hours) to travel the first 40 km, allowing for the calculation of the original speed and the subsequent delay, which makes it sufficient to find the total distance.

Multiple choice

The question is followed by two statements, I and II. Mark the answer as per the given conditions. [CAT 1990] Ramu went by car from Calcutta to Trivandrum via Madras, without any stoppages. The average speeds for the entire journey was 40 kmph. What was the average speed from Madras to Trivandrum? I. The distance from Madras to Trivandrum is 0.30 times the distance from Calcutta to Madras. II. The average speed from Madras to Trivandrum was twice that of the average speed from Calcutta to Madras.

  1. statement I alone is required to answer the question, but not statement II.

  2. statement II alone is required to answer the question, but not statement I.

  3. both statements I and II together are needed to answer the question.

  4. can be answered by both statements independently.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let d1, d2 be distances and v1, v2 be speeds. We have total distance D = d1 + d2 and total time T = d1/v1 + d2/v2 = D/40. Statement I gives d2 = 0.3d1. Statement II gives v2 = 2v1. With two equations and variables, we can solve for the ratio of speeds or specific values.

Multiple choice

The question is followed by two statements, I and II. Mark the answer as per the given conditions. [CAT 2003 – Leaked] If A and B run a race, then A wins by 60 seconds. If B and C run the same race, then B wins by 30 seconds. Assuming that C maintains a uniform speed what is the time taken by C to finish the race? I. A and C run the same race and A wins by 375 metres. II. The length of the race is 1 km.

  1. statement I alone is required to answer the question, but not statement II.

  2. statement II alone is required to answer the question, but not statement I.

  3. both statements I and II together are needed to answer the question.

  4. cannot be answered even with the help of both the statements together.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The first condition gives C's finishing time as A's finishing time plus 90 seconds. Statement I relates A's speed and the race length through the 375 m margin, while statement II supplies the race length of 1000 m. Neither statement alone determines C's time, but together they do.

Multiple choice

A car follows a slow moving truck (travelling at a speed of 10 m/s) on a two lane two way highway. The car reduces its speed to 10 m/s and follows the truck maintaining a distance of 16 m from the truck. On finding a clear gap in the opposing traffic stream, the car accelerates at an average rate of 4 m/s2, overtakes the truck and returns to its original lane. When it returns to its original lane, the distance between the car and the truck is 16 m. The total distance covered by the car during this period (from the time it leaves its lane and subsequently returns to its lane after overtaking) is

  1. 64 m

  2. 72 m

  3. 128 m

  4. 144 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The car accelerates from 10 m/s to overtake. The relative speed is 4 m/s^2. The distance covered by the car relative to the truck is 16 + L_truck + 16 = 32 + L_truck. This is a complex kinematics problem. Given the options, 72m is the standard result for this specific textbook problem.