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Time, Speed and Distance Exercise 2

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  • Most Important Multiple Choice Questions
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  1. Question 1 of 25
    1. Question

    The speed of a car increases by 2 kms after every one hour. If the distance travelled in the first one hour was 35 kms, what was the total distance travelled in 12 hours?

    Hint

    Total distance travelled in 12 hour

    = (35 + 37 + 39 + ….. upto 12 terms)

    This is an A.P. with first term a = 35,

    number of terms n = 12,

    common difference d = 2.

    ∴ Required distance

    = time-and-distance-q-67767.png

  2. Question 2 of 25
    2. Question

    Anna left for city A from city B at 5.20 a.m. She travelled at the speed of 80 km/h for 2 hours 15 minutes. After that the speed was reduced to 60 km/h. If the distance between two cities is 350 kms, at what time did Anna reach city A?

    Hint

    Distance covered in 2 hr 15 min,

    i.e., 2¼ hrtime-and-distance-q-67737.png

    Time taken to cover remaining distance

    = time-and-distance-q-67731.png

    = 2 hr 50 min.

    Total time taken

    = (2 hr 15 min + 2 hr 50 min)

    = 5 hr 5 min.

    So, Anna reached city A at 10.25 a.m.

  3. Question 3 of 25
    3. Question

    A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9 : 30 a.m.?

    Hint

    Relative speed

    = (2 + 3) = 5 rounds per hour.

    So, they cross each other 5 times in an hour and 2 times in half an hour.

    Hence, they cross each other 7 times before 9 :.30 a.m.

  4. Question 4 of 25
    4. Question

    A circular running path is 726 metres in circumference. Two men start from the same point and walk in opposite directions @ 3.75 km/h and 4.5 km/h, respectively. When will they meet for the first time?

    Hint

    Their relative speeds

    = (4.5 + 3.75) = 8.25 km/h

    Distance = 726 metres

    = time-and-distance-q-68030.png

    Required time

    = time-and-distance-q-68024.png min

  5. Question 5 of 25
    5. Question

    A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, his speed (in km/h) must be:

    Hint

    Remaining distance = 3 km

    and remaining time

    = time-and-distance-q-68018.png

    ∴ Required speed = (3 × 4) km/h

    = 12 km / hr.

  6. Question 6 of 25
    6. Question

    In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:

    Hint

    Let the duration of the flight be x hour Then,

    time-and-distance-q-68012.png

    ⇒ x (2x + 1) = 3

    ⇒ 2x² + x – 3 = 0

    ⇒ (2x + 3) (x – 1) = 0

    ⇒ x = 1 hr. [neglecting the –ve value of x].

  7. Question 7 of 25
    7. Question

    A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?

    Hint

    Relative speed of the thief and policeman

    = (11 – 10) km/h = 1 km/h.

    Distance covered in 6 minutes

    = time-and-distance-q-68006.png

    ∴ Distance between the thief and policeman

    = (200 – 100) m = 100 m.

  8. Question 8 of 25
    8. Question

    Two persons living in different towns 32 km apart started at 1 pm to see each other at the rate of 3.5 and 4.5 km per hour respectively. When will they meet?

    Hint

    Relative speed

    = (3.5 + 4.5) = 8 kmph.

    Time to meet = 32/8 = 4 hour

    So when they meet at 5 pm, one will have walked

    3.5 × 4 = 14 km and the other will have walked

    4.5 × 4 = 18 km.

  9. Question 9 of 25
    9. Question

    A man rides at the rate of 11 miles an hour, but stops for 5 min to change horse at the end of every seventh mile. How long will be take to go a distance of 96 miles? (Approx.)

    Hint

    time-and-distance-q-67999.png

    Time taken to travel 96 miles

    = ⁹⁶⁄₁₁ hr = 8 hr 43 minutes

    During the journey of 96 miles, he has to stop for 13 times to change the horse.

    ∴Total stoppage time

    = 13 × 5 = 65 mins. = 1 hr. 5 mins.

    Hence the total time

    = 8 hr 43 mins + 1 hr. 5 mins.

    = 9 hr 48 mins.

  10. Question 10 of 25
    10. Question

    Subbu starts from a point O at 10:00 a.m., overtakes Ajay, who is moving in the same direction, at 11:00 a.m. and Bhuvan moving in the opposite direction at 12:00 (noon). If the speed of Bhuvan is one fourth the speed of Subbu, at what time will Ajay and Bhuvan cross each other?

    Hint

    Let the speed of Ajay be V and the speed of Bhuvan and Subbu be 1 and 4 respectively.

    Then OA = 4 and OB = 4.

    At 12:00 noon.

    time-and-distance-q-67992.png

    Let Ajay be at C at 12:00 noon at a distance of V from A (towards B)

    ∴ Time taken for them to meet from 12:00 noon. = time-and-distance-q-67986.png

    Since V is not known time-and-distance-q-67979.pngcannot be determined.

  11. Question 11 of 25
    11. Question

    On a journey across Bombay, a tourist bus averages 10 km/h for 20% of the distance, 30 km/h for 60% of it and 20 km/h for the remainder. The average speed for the whole journey was

    Hint

    Let the average speed be x km/h.

    and total distance = y km. then,

    time-and-distance-q-68400.png

    time-and-distance-q-68394.png

  12. Question 12 of 25
    12. Question

    A man walks half of the journey at 4 km/h by cycle does one third of journey at 12 km/h and rides the remainder journey in a horse cart at 9 km/h, thus completing the whole journey in 6 hours and 12 minutes. The length of the journey is

    Hint

    Let the length of the journey =x km.

    ∴ Journey rides by horse cart

    time-and-distance-q-68387.pngtime-and-distance-q-68381.png

    Then, total time taken to complete journey

    time-and-distance-q-68375.png

    time-and-distance-q-68369.png

    time-and-distance-q-68362.png

    time-and-distance-q-68355.png

  13. Question 13 of 25
    13. Question

    A train leaves station X at 5 a.m. and reaches station Y at 9 a.m. Another train leaves station Y at 7 a.m. and reaches station X at 10: 30 a.m. At what time do the two trains cross each other?

    Hint

    Let the distance between X and Y be x km.

    Then, the speed of A is x/4 km/h and that of B is 2x/7 km/h.

    time-and-distance-q-68337.png

    Relative speeds of the trains

    = time-and-distance-q-68331.png

    Therefore the distance between the trains at 7 a.m.

    = time-and-distance-q-68324.png

    Hence, time taken to cross each other

    = time-and-distance-q-68318.png

    Thus, both of them meet at 7 : 56 a.m.

  14. Question 14 of 25
    14. Question

    A man covers a certain distance on a toy train. If the train moved 4 km/h faster, it would take 30 minutes less. If it moved 2 km/h slower, it would have taken 20 minutes more. Find the distance.

    Hint

    Let the distance be x km. Let speed of train be y km/h. Then by question, we have

    time-and-distance-q-68312.png …(i)

    and time-and-distance-q-68305.png …(ii)

    On solving (i) and (ii), we get x = 3y

    Put x = 3y in (i) we get

    time-and-distance-q-68299.png

    ⇒ y = 20

    Hence, distance = 20 × 3 = 60 km.

  15. Question 15 of 25
    15. Question

    If a man walks to his office at 5/4 of his usual rate, he reaches office 30 minutes early than usual. What is his usual time to reach office.

    Hint

    time-and-distance-q-68293.png

    time-and-distance-q-68287.png

  16. Question 16 of 25
    16. Question

    Mary jogs 9 km at a speed of 6 km per hour. At what speed would she need to jog during the next 1.5 hours to have an average of 9 km per hour for the entire jogging session?

    Hint

    Let speed of jogging be x km/h.

    Total time taken

    time-and-distance-q-68281.png

    Total distance covered = (9 + 1.5x) km.

    time-and-distance-q-68275.png

    time-and-distance-q-68269.png

  17. Question 17 of 25
    17. Question

    Mohan travels 760 km to his home, partly by train and partly by car. He takes 8 hours if he travels 160 km by train and the rest by car. He takes 12 minutes more if he travels 240 km by train and the rest by car. The speed of the train and the car, respectively are:

    Hint

    Let speed of the train be x km/h and that of the car be y km/h.

    Now, time-and-distance-q-68263.png …(i)

    and time-and-distance-q-68257.png …(ii)

    Solving (i) and (ii),

    we have x = 80 km/h and

    y = 100 km/h.

  18. Question 18 of 25
    18. Question

    It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the speed of the car is :

    Hint

    Let the speed of the train and the car be x km/h and y km/h, respectively.

    Now, time-and-distance-q-68251.png …(i)

    and time-and-distance-q-68245.png …(ii)

    From (i),

    120y + 480x = 8xy and …(iii)

    From (ii),

    200y + 400x = time-and-distance-q-68239.png …(iv)

    From (iii) and (iv),

    time-and-distance-q-68233.png

    ⇒ 15y + 60x = 24y + 48x

    ⇒ 12x = 9y

    ⇒ time-and-distance-q-68226.png

  19. Question 19 of 25
    19. Question

    In a flight of 6000 km, an aircraft was slowed down due to bad weather. The average speed for the trip was reduced by 400 kmph and the time of flight increased by 30 minutes. The original planned duration of the flight was

    Hint

    Let the original planned time of the flight be x hour

    ∴ The average speed of the flight

    = time-and-distance-q-68220.png km/h

    If the average speed is

    time-and-distance-q-68214.png km/h,

    then the time of the flight is

    time-and-distance-q-68208.png hour

    ∴ time-and-distance-q-68202.png

    ⇒ – 400x + time-and-distance-q-68196.png

    ⇒ – 4x + time-and-distance-q-68190.png

    ⇒ – 4x² + 30 – 2x = 0

    ⇒ 4x² + 2x – 30 = 0

    ⇒ 2x² + x – 15 = 0

    ⇒ x = time-and-distance-q-68184.png

    = time-and-distance-q-68178.png

  20. Question 20 of 25
    20. Question

    Points A and B are 70 km apart on a highway. One car starts form A and the another one from B at the same time. If they travel in the same direction, they meet in 7 hours But if they travel towards each other, they meet in one hour. The speeds of the two cars are, respectively.

    Hint

    Let the speed of the car be x km/h and y km/h, respectively.

    Their relative speeds when they are moving in same direction = (x – y) km/h.

    Their relative speeds when they are in opposite directions = (x + y) km/h.

    Now, time-and-distance-q-68172.png

    or x + y = 70 … (i)

    and time-and-distance-q-68166.png or x – y = 10 … (ii)

    Solving (i) and (ii), we have

    x = 40 km/h and y = 30 km/h.

  21. Question 21 of 25
    21. Question

    A plane left 30 minutes later than the scheduled time and in order to reach the destination 1500 km away in time, it had to increase the speed by 250 km/h from the usual speed. Find its usual speed.

    Hint

    Let the usual speed of the plane be x km/h

    ∴ Time taken in covering the distance of 1500 km

    =1500/x hour

    ∴ time-and-distance-q-68160.png

    ⇒ 3000 x = 3000 (x + 250) – x(x + 250)

    ⇒ x² + 250 x – 3000 × 250 = 0

    ⇒ time-and-distance-q-68153.png

    = time-and-distance-q-68147.pngkm/h

  22. Question 22 of 25
    22. Question

    Walking ⁶⁄₅ of his usual speed, a person takes 10 min less to reach his office. His usual time taken to reach the office is

    Hint

    time-and-distance-q-68141.png

  23. Question 23 of 25
    23. Question

    A man starts from B to K, another from K to B at the same time. After passing each other they complete their journeys in 3⅓ and 4⅘ hours, respectively. Find the speed of the second man if the speed of the first is 12 km/hr.

    Hint

    time-and-distance-q-68135.png

    = time-and-distance-q-68129.png

    = time-and-distance-q-68123.png

    = time-and-distance-q-68117.png

    = time-and-distance-q-68111.png = ⁶⁄₅

    ∴ time-and-distance-q-68104.png = ⁶⁄₅

    ∴ 2nd man’s speed

    = ⁶⁰⁄₆ = 10 km/hr.

  24. Question 24 of 25
    24. Question

    A man travelled a distance of 50 km on his first trip. On a later trip, travelling three times as fast, he covered 300 km. Compare the times he took.

    Hint

    Let speed be x

    ⇒50/x = time taken

    also time-and-distance-q-68098.png = time taken.

    Hence ratio is 1 : 2.

  25. Question 25 of 25
    25. Question

    The driver of a car driving @ 36 kmph locates a bus 40 meters ahead of him. After 20 seconds the bus is 60 meters behind. The speed of the bus is :

    Hint

    Net distance gained by car over the bus

    = 40 + 60 = 100m, in 20 sec.

    Time = time-and-distance-q-68092.png

    ⇒ S₂ = 5 m/s = 18 kmph.

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