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

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Each of the questions below consists of a question and two statements I, and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer.

Two trains P and Q are travelling towards each other on the same track. The initial distance between them is 91 km. Find the time, when the two trains will collide. Statement I : The speed of train P is 65km/h and the speed of Q is 104 km/h more than that of train P. Statement II : The ratio of speeds of the two trains is 5 : 13.

  1. If 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.

  2. If 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.

  3. If the data either in statement I alone or in statement II alone is sufficient to answer the question.

  4. If the data in both statements I and II together are necessary to answer the question.

  5. If the data given in both statements I and II together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I gives both speeds: P = 65 km/h, Q = 65 + 104 = 169 km/h. Combined speed = 234 km/h, distance = 91 km. Time = 91/234 hours. This is sufficient. Statement II only gives the ratio 5:13, which gives the same relative speeds but no absolute values to calculate the time.

Multiple choice

Passage

Each of the questions below consists of a question and two statements given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer.

Find the distance travelled by Rajdhani express in two hours if it travels with its original speed? I. The train started from the origin station 20.25 hours later than the scheduled time towards its destination which is 750 km away from the origin. II. To reach the destination station in the scheduled time the loco – piolet of the train increases the speed of the train to 125% of the original speed.

  1. If Statement I alone is sufficient to answer the question

  2. If Statement II alone is sufficient to answer the question

  3. If Both the Statements I and II together are needed to answer the question.

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

  5. Both statements together are not sufficient to answer
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Both statements together are needed. Statement I gives delay (20.25 hours) and distance (750 km) but not speed. Statement II gives speed increase (125% of original) but not distance or delay. Together: 750/S - 750/(1.25S) = 20.25, giving original speed S, then 2-hour distance = 2S.

Multiple choice

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The following questions are accompanied by two statements A and B. You have to determine which statements(s) is/are sufficient/necessary to answer the questions.

Find the speed of boat in still water. (A) time taken to cover a distance of 18 km, first in upstream, then in downstream is 4 ½ hours. (B) If the speed of current gets doubled, then time taken to cover 18 km, first in downstream, then in upstream is 7 ⅕ hours.

  1. Statement A alone is sufficient to answer the question, but statement B alone is not sufficient to answer the questions.

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

  3. Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question.

  4. Either statement A or statement B by itself is sufficient to answer the question.

  5. Statements A and B taken together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed be b and current speed be c. Statement A gives 18/(b-c) + 18/(b+c) = 4.5. Statement B gives 18/(b+2c) + 18/(b-2c) = 7.2. Both equations are needed to solve for the two variables b and c.

Multiple choice

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S.111-115) Directions for questions: 2 trains start from A and B and move towards B and A respectively. Train from A starts at 8 am and reaches B at 4 pm while train from B starts at 10 am and reaches A at 10 pm. Also, Train from A crosses a platform 200 m long in 10 seconds and a man moving in the same direction at 5 m/sec in 5 seconds.

Q.112) If train A maintains a constant and consistent speed during the journey, what is the distance between stations A and B?

  1. a) 2000 km

  2. b) 1300 km

  3. c) 1280 km

  4. d) 1008 km
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Train A: 8 am to 4 pm (8 hours). Train B: 10 am to 10 pm (12 hours). Let distance be D. Speed A = D/8, Speed B = D/12. Relative speed = D/8 + D/12 = 5D/24. They meet at a time determined by the 2-hour gap. The calculation leads to 1008 km.

Multiple choice

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Directions: Study the given data carefully and answer the following question. Three trains are standing at the same platform. The data regarding the three trains are given below. Train P: It travels 20% less distance than R. Train Q: It travels 420 km at a speed of 60 km/hr. Train R: It travels for 10 hours and has 10% more speed than train Q.

If the speed of train Q increases by 40%, then how much time will train Q save if it covers the same distance?

  1. 2 hours

  2. 1 hour

  3. 1.5 hours

  4. 2.5 hours

  5. 3 hours
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Train Q travels 420 km at 60 km/hr, taking 7 hours. If speed increases by 40%, new speed = 60 * 1.4 = 84 km/hr. New time = 420 / 84 = 5 hours. Time saved = 7 - 5 = 2 hours.

Multiple choice

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Directions: Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You are to use the given data and your knowledge of Mathematics to choose among the given options.

Quantity I: The distance from point A to B is 156 km and a ferry takes a round trip and completes the same in 12 hours and 30 minutes. It is given that the ratio of the speed of the ferry in still water to the stream speed is 8 : 5. Calculate the speed of the ferry in still water. Quantity II: Roger travels at the speed of 84 km/hr for 6 hours and at 72 km/hr for 4 hour. Calculate his average speed for the journey of 10 hours.

  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 can be established.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Round trip distance = 312 km. Total time = 12.5 hours. Let speed in still water be 8x and stream be 5x. Downstream = 13x, Upstream = 3x. 156/13x + 156/3x = 12.5 => 12/x + 52/x = 12.5 => 64/x = 12.5 => x = 5.12. Still water speed = 8 * 5.12 = 40.96 km/h. Quantity II: Average speed = Total distance / Total time = (84*6 + 72*4) / 10 = (504 + 288) / 10 = 79.2 km/h. Thus, I < II.

Multiple choice

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1695471_passage_1531734788_hindi.htm

Directions: In the following question, you have to find out which of the following statements is/are redundant for determining the answer of the given question. What is the speed of boat in still water? Statements: I. The boat covers 12 km in 2 hr downstream. II. The boat covers the same distance in 4 hr upstream. III. The speed of the stream is one-third that of the boat in still water.

  1. Both I and II

  2. Either II or III

  3. Only III

  4. The question cannot be answered even with the information in all three statements

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

Let boat speed be B and stream speed be S. I: B+S = 12/2 = 6. II: B-S = 12/4 = 3. III: S = B/3. From I and II, 2B = 9, B = 4.5. From I and III, B + B/3 = 6 => 4B/3 = 6 => B = 4.5. From II and III, B - B/3 = 3 => 2B/3 = 3 => B = 4.5. Any two statements are sufficient to find B. Therefore, any one statement is redundant.

Multiple choice

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Directions: Read the following information and answer the given question. Trains A and B run between stations P, Q and R. These stations are in the same line, station Q is between stations P and R. The total distance between stations P and R is 300 km. The ratio of the distance between stations P and Q and stations Q and R is 3 : 2. Train A starts from station P and train B starts from station Q and both travel towards station R. Train B starts two hours after train A.

If the trains A and B meet at a distance of 200 km from station P and train A is running with a speed of 60 km/h, then what would be the speed of train B?

  1. 10 km/h

  2. 12 km/h

  3. 15 km/h

  4. 18 km/h

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

Passage

Directions: Read the following information and answer the given question. Trains A and B run between stations P, Q and R. These stations are in the same line, station Q being between stations P and R. The total distance between stations P and R is 300 km. The ratio of the distance between stations P and Q to that between stations Q and R is 3 : 2. Train A starts from station P and train B starts from station Q, and both travel towards station R.

On one day, both trains A and B start at the same time; their speeds are 5t km/hr and 4t km/hr, respectively. Train A goes non-stop till station R, while train B stops in between for 2t minutes before reaching station R. If both trains reach R at the same time, then what is the value of t?

  1. 15

  2. 30

  3. 45

  4. 60
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

PQ:QR = 3:2. Total 300km, so PQ = 180km, QR = 120km. Train A (P to R) = 300km at 5t km/hr. Time = 300/(5t) = 60/t hours. Train B (Q to R) = 120km at 4t km/hr. Time = 120/(4t) + (2t/60) hours. 60/t = 30/t + t/30. 30/t = t/30, so t^2 = 900, t = 30.

Multiple choice

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What is the speed of stream?

(A) Sum of time taken by a boat in upstream and downstream is 27 hours to cover distance 270 km in each. (B) Speed of boat in downstream is 45 km/h. (C) Boat cover 90 km in 7 hr, while rowing in upstream

  1. (a)Either A and B or B and C Are sufficient to answer the question

  2. (b) Either A and B or A and C Are sufficient to answer the question

  3. (c) Either A and C or B and C Are sufficient to answer the question

  4. (d) Any two statements are sufficient to answer the question

  5. (e) Either only A or B and C together are sufficient to answer the question
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let boat speed be B and stream speed be S. (A) 270/(B-S) + 270/(B+S) = 27. (B) B+S = 45. (C) 90/(B-S) = 7. Using C, B-S = 90/7. With B+S = 45, we can solve for S. Using A and B, we can also solve for S. Any two statements provide enough info to solve for B and S.

Multiple choice

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[CAT 1997] Directions for Questions 27 to 29: Answer the questions based on the following information. Boston is 4 hr ahead of Frankfurt and 2 hr behind India. X leaves Frankfurt at 6 p.m. on Friday and reaches Boston the next day. After waiting there for 2 hr, he leaves exactly at noon and reaches India at 1 a.m. On his return journey, he takes the same route as before, but halts at Boston for 1 hr less than his previous halt there. He then proceeds to Frankfurt.

If his journey, including stoppage, is covered at an average speed of 180 mph, what is the distance between Frankfurt and India?

  1. 3,600 miles

  2. 4,500 miles

  3. 5,580 miles

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Passage

[CAT 2000] Directions for Questions 5 and 6: There are five machines A, B, C, D and E situated on a straight line at distances of 10 metres, 20 metres, 30 metres, 40 metres and 50 metres respectively from the origin of the line. A robot is stationed at the origin of the line. The robot serves the machines with raw material whenever a machine becomes idle. All the raw material is located at the origin. The robot is in an idle state at the origin at the beginning of a day. As soon as one or more machines become idle, they send messages to the robot-station and the robot starts and serves all the machines from which it received messages. If a message is received at the station while the robot is away from it, the robot takes notice of message only when it returns to the station. While moving, it serves the machines in the sequence in which they are encountered, and then returns to the origin, If any messages are pending at the station when it returns, it repeats the process again. Otherwise, it remains idle at the origin till the next message(s) is (are) received.

Suppose on a certain day, machines A and D have sent the first two messages to the origin at the beginning of the first second, and C has sent a message at the beginning of the 5th second and B at the beginning of the 6th second, and E at the beginning of the 10th second. How much distance in metres has the robot travelled since the beginning of the day, when it notices the message of E? Assume that the speed of movement of the robot is 10 metres per second.

  1. 140

  2. 80

  3. 340

  4. 360
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The robot serves machines in order of distance. At t=0, A(10m) and D(40m) are waiting. Robot travels to D (40m) and back (40m), total 80m. At t=5, C(30m) is waiting. Robot travels to C(30m) and back(30m), total 60m. Total distance = 80 + 60 = 140m. The robot notices E at the origin after returning from C.

Multiple choice

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Directions for questions 61 to 64: Read the information provided and answer the questions that follow. Praveen, who is interested in numismatics, came across some old coins 200 km away from his home, in an old town and drove at a speed double that of his regular speed with which he drove backwards to his home after collecting them. He then travelled to the archaeological department office, 15 km from his home, and reached in 20 min. After 45 min, he travelled to Govt. Information office located at 30 km away from the archaeological office, with his regular speed and had a meeting there for 30 min. He drove back to his home after meeting on the same route.

  1. What is the average speed of his entire journey from home to Government information office & return including the time he spent in between?

  1. a) 15.3kmph

  2. b) 21.4kmph

  3. c) 27.7kmph

  4. d) 32.5kmph
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Passage

Directions: Answer the question based on the following information. Table 1 gives the men's and women's world record times for various outdoor running distances, recognized by the International Association of Athletics Federations (IAAF) as of 17 November 2017. Table 1: World record running times data Running distance (D) (meters (m)) Men's record (M) (seconds (s)) Women's record (W) (Seconds (s)) 100 9.6 10.5 200 19.2 21.3 400 43 47.6 800 101 113.3 1,000 132 149 1,500 206 230.1 2,000 284.8 323.8 3,000 440.7 486.1 5,000 757.4 851.2 10,000 1,577.5 1,757.5

If α is the factor by which the women's world record average speed reduces with doubling of the running distance, the smallest value of α occurs for the pair of categories:

  1. (100 m, 200 m)

  2. (1,500 m, 3,000 m)

  3. (5,000 m, 10,000 m)

  4. (400 m, 800 m)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If speed reduces by a factor of alpha, then the new speed is the old speed divided by alpha, meaning alpha equals the old speed divided by the new speed. Calculating this ratio for each option, we find the values are 1.014 for (100 m, 200 m), 1.056 for (1,500 m, 3,000 m), 1.032 for (5,000 m, 10,000 m), and 1.190 for (400 m, 800 m). The smallest value of alpha is 1.014, which occurs for the pair (100 m, 200 m).

Multiple choice

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Directions: The three planes on a same airport travels to different destination by different routes. The data of 3 planes is given below. Plane M = Its speed is 800 km/hr and time taken by plane M is 20% more than Plane O. Plane N = It travels 25% less distance than plane M. Plane O = It covered 4,800 km in 8 hours.

What is the time taken by plane N if its speed is 750 km/hr?

  1. 9.2 hours

  2. 7.68 hours

  3. 8.5 hours

  4. 9.6 hours

  5. 10 hours
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Plane O: 4800 km / 8 hr = 600 km/hr. Plane M: Time = 1.2 * 8 hr = 9.6 hr. Distance M = 800 * 9.6 = 7680 km. Plane N: Distance = 0.75 * 7680 = 5760 km. Time N = 5760 / 750 = 7.68 hr.