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Examveda

Two buses start from a bus terminal with a speed of 20 km/h at interval of 10 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at interval of 8 minutes?

A. 3 km/h

B. 4 km/h

C. 5 km/h

D. 7 km/h

Answer: Option C

Solution(By Examveda Team)

Let Speed of the man is x kmph.
Distance covered in 10 minutes at 20 kmph = distance covered in 8 minutes at (20 + x) kmph.
Or, $$20 \times \frac{{10}}{{60}} = \frac{8}{60}\times\left(20+x\right) $$
Or, 200 = 160 + 8x
Or, 8x = 40
Hence, x = 5kmph.

Detailed Explanation:
A _____________M_______________B
A = Bus Terminal.

B = Let meeting point of first bus and the man and this distance is covered by Bus in 10 minutes. I.e. Distance A to be is covered first bus in 10 min. As AB distance can be covered by second bus in 10 minutes as well.

Distance Covered by Bus in 10 min = AB = $$\frac{{20}}{{60}} \times 10$$   = $$\frac{{10}}{3}$$ km.

Now, M is the Meeting Point of Second Bus with Man. Man covered distance B to M in 8 minutes.
Now, Relative distance of both Man and Bus will be same as both are traveling in opposite direction of each other. Let Speed of the man = x kmph.

Relative speed = 20 + x

To meet at Point M, bus and Man has covered the distance (AB) in 8 minutes with relative speed. And Same AB distance is covered by bus in 10 minutes. Thus, Distance covered in 8 minutes with relative speed (20 + x) kmph = distance covered by bus in 10 minuted with speed 20 kmph.

This Question Belongs to Arithmetic Ability >> Speed Time And Distance

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Comments ( 27 )

  1. Shomsher John
    Shomsher John :
    2 years ago

    Distance travelled by man in 8 mins and distance travelled by bus in 2 mins must be equal.

    So, Distance travelled by Bus in 2 mins would be 20 x 2/60 = 2/3

    In a same way, Distance travelled by man in 8 mins will become = X x 8/60

    Now, 2/3 = 8X/60 (because both speeds should be same)

    24x = 120 (by Cross Multiplying)

    x = 120/24

    x = 5 Answer

  2. Harshada Chhallani
    Harshada Chhallani :
    2 years ago

    1) find distance b/w both buses in their interval of 10 min = speed*interval =(20km0min) *10min =3.33km
    (interval distance of 3.33km b/w busses is distance covered by man and 2nd bus in their combine speed)
    2) find combine speed of man and 2nd bus = (3.33km/8min)*60min =24.9 km/hr
    3) find man's speed from combine speed = 24.9- bus speed = 24.9-20 = 4.9 ~ 5 km/hr

  3. Ashish
    Ashish :
    2 years ago

    10/3

    Speed(X+Y)= 10×60/3×8= 25

    25-20= 5

  4. FACTOM WORLD
    FACTOM WORLD :
    3 years ago

    Good explanation in the commens

  5. Nikhil Sharma
    Nikhil Sharma :
    3 years ago

    If i have to shiw in the diagram the how can i show the relative speed with yhe help og the diagram

  6. Bibhuti
    Bibhuti :
    3 years ago

    Total distance travelled by both (BUS+MAN) to meet each other => total distance covered by BUS (only) at the speed of 20 k/h in 10 mins. So, Distance between them = 20*(10/60) = 20/6 km.
    ATQ, BUS and MAN travelling in opposite direction and meet after 8 min.
    So, as we know S = D/T, It should be like = (20/6) / (20+x) = 8/60 (Let, speed of the man is x km/h)
    => x = 5 km/hr.
    Hope this will help you to understand and visualize the concept of this question.

  7. Vaibhav Gupta
    Vaibhav Gupta :
    3 years ago

    It can be solved easily in 3-4 lines using frame of reference concept.

  8. Santosh Nani
    Santosh Nani :
    3 years ago

    1st bus starts and after 10min 2nd bus starts.
    Man is moving in opposite direction. If man doesn't move he would have met the second bus exactly at 10th min
    As man is moving with some speed in opposite direction definitely he will be meeting the 2nd bus taking time less than 10min i.e 8min as mentioned in the question
    After man meeting the 1st bus consider the relative speed between man and the 2nd bus.

    Let the speed of man be 'x' km/hr and speed of 2nd bus is 20km/hr(given)

    The distance travelled by the man and 2nd bus in 8min is the distance travelled by the 2nd bus in 10min

    Distance travelled by the man and 2nd bus in 8min is (x+20)8

    Now (x+20)8=20*10
    By solving x=5km/hr (speed of man)

  9. Aks Singh
    Aks Singh :
    3 years ago

    A bus starts from X to Y at 40 kmph. Half an hour later another bus leaves Y for X travelling at 45 kmph. If the distance from X to Y is 105 km, how far from X will the buses meet? *

  10. Mohit Rana
    Mohit Rana :
    4 years ago

    Time 10 min se 8 min krna h... 2 km hora 10 m 1/5 se time km hora to 1/4 se speed bdhani hogi... 20*1/4=5kmph

    Time. 10:8
    Speed. 4:5
    4 20kmph k brabr h to 5 25 kmph k brabr hoga...

  11. Noor Hasan
    Noor Hasan :
    4 years ago

    There should be a correction
    (20+x) should be written as numerator

  12. Anoushka Singh
    Anoushka Singh :
    4 years ago

    I still don't understand the concepts

  13. Saumyojit Das
    Saumyojit Das :
    4 years ago

    Distance travelled by bus1 in 10 minutes= 20 km/hr / (10/60) =3.33 km
    bus2 and bus 1 have constant 3.33 km difference due to their constant speed and now man travels 3.33km in 8 minutes from bus1 to 2 . so his speed is 3.33 km / (8/60) =25km/hr
    relative speed in opposite shuld be plus or minus??= 25-20 = 5km/hr

  14. Kumar Nath
    Kumar Nath :
    4 years ago

    Correction needed, 20+x would be multiply with 8 as like below
    20*10/60=(20+x)*8/60

  15. Bipul Banik
    Bipul Banik :
    5 years ago

    I m not clear.can anyone expain with a graphical explanation?

  16. Living Dreamz
    Living Dreamz :
    5 years ago

    M:b
    t 8:2
    s 2:8
    According to question,
    8u=20
    Then
    1u=5/2
    Then 2u= 5/2×2=5

  17. Anand Krishnan
    Anand Krishnan :
    6 years ago

    Is it correct to say that point 'B' should come in b/w points 'A' & M' ?

  18. SUNIL KUMAR
    SUNIL KUMAR :
    6 years ago

    M:B
    t. 8:2
    S 2:8
    20÷8×2=5 km/h
    Which is speed of man.

  19. Krishna Pothalahujuj
    Krishna Pothalahujuj :
    6 years ago

    another better way to solve the problem

  20. Longkiri Tisso
    Longkiri Tisso :
    7 years ago

    what annual payment will discharge a debt of rs.6550 due in 4 years at 5% per annum simple interest?

  21. Abhik Ranu
    Abhik Ranu :
    7 years ago

    solution will be

    20*10/60 = 8(20+x)/60
    Or, 200 = 160+8x
    Or, 8x = 40
    Hence, x = 5kmph.

    but on the above " {8/60(20+x)} " was done. but the right process is " {8(20+x)/60} "

  22. Kumar Chandan
    Kumar Chandan :
    8 years ago

    The relative distance covered by Bus and Man in 8 minutes should be equal to distance covered by bus in 10 minutes. I.e

    Distance covered by bus and man together with relative speed 20 + x kmph = distance covered by bus in 10 minutes.

  23. Manas Sarangi
    Manas Sarangi :
    8 years ago

    Sir e question ka answer kese aya.how a distance cover by a man and bus same hoga

  24. Sai Kamal
    Sai Kamal :
    8 years ago

    i was not clear with the solution ,can anyone help me ?

  25. Aisha Gupta
    Aisha Gupta :
    8 years ago

    How can you equal these distances. Give me a logic

  26. Mohit
    Mohit :
    8 years ago

    Where its mentioned the distance covered by bus and man are same ???

  27. Pekay
    Pekay :
    8 years ago

    very good

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