Quantitative Aptitude: Time, Speed and Distance Set 19

  1. A person sees a train passing over 3km long bridge. The length of the train is half that of bridge if the train clears the bridge in 4mins. What is the speed of the train ?
    67.5 km/hr
    50 km/hr
    62 km/hr
    48 km/hr
    None of these
    Option A

    Distance covered in 4/60 hours = (3 + 3/2) = 9/2 km
    Distance covered in 1 hour = (9/2) x (60/4) = 67.5km/hr.
    So, speed of the train = 67.5 km/hr

     

  2. Two trains X and Y start at the same time in the opposite direction from two points P and Q and arrive at their destinations 36 and 25 hours respectively after their meeting each other. At what speed does the second train Y travel if the first train travels at 80 km/h.
    80 km/hr
    90 km/hr
    70 km/hr
    96 km/hr
    60 km/hr
    Option D
    Let the speed and time of two trains be s1 and s2, and t1 and t2.
    s1/s2 = (t2/t1)1/2
    => 80/s2 = 5/6
    => s2 = 96km/hr.

     

  3. Two trains are running at 60 km/hr and 40 km/hr respectively in the same direction. Faster train completely passes a man sitting in the slower train in 54 seconds. What is the length of the fast train?
    100 m
    150 m
    300 m
    200 m
    250 m
    Option C
    Relative speed = (60 – 40) km/hr = 20km/hr.
    Length of the faster train = (20*54*5)/18 = 300m

     

  4. There are two goods trains each 1000 m long are running in opposite directions on parallel tracks. Their speeds are 55 km/hr and 35 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
    50 sec.
    80 sec.
    60 sec.
    90 sec.
    70 sec.
    Option B
    Relative speed = 55 + 35 = 90 km/hr. =90 * 5/18 = 25 m/sec.
    Distance covered = 1000 + 1000 = 1000 m.
    Required time = 2000 / 25 = 80 sec.

     

  5. A truck running from a city at a speed of 40 km/hr and the speed of the truck was increased by 2 km/hr at the end of every hour. Find the total distance covered by the truck in the first 5 hours of the journey.
    180 km
    120 km
    220 km
    90 km
    105 km
    Option C
    The total distance covered by the truck in the first 5 hours = 40 + 42 + 44 + 46 + 48
    sum of five terms in AP whose first term is 40 and last term is 48 = 5/2 [40 + 48] = 220 km.

     

  6. Two persons start running simultaneously around a rectangular track of length 700 m from the same point at speeds of 45 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
    50 sec.
    42 sec.
    25 sec.
    36 sec.
    40 sec.
    Option D
    Time taken to meet for the first time = length of the track / relative speed = 700 / (45 + 25)
    = (700*18)/(70*5) = 36 sec.

     

  7. A train departs Kolkata at 6 a.m. at a speed of 40 kmph. After one hour, another train departs Kolkata in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Kolkata do the two trains meet?
    10 a.m. & 200 km
    10 a.m & 122 km
    10:10 a.m & 210 km
    11 a.m & 200 km
    None of these
    Option A
    When the second train departs Kolkata the first train covers 40 * 1 = 40 km
    So, the distance between first train and second train is 40 km at 7.00am
    Time taken by the trains to meet = Distance / relative speed
    = 40 / (50 -40) = 4 hours
    So, the two trains meet at 10 a.m.
    The two trains meet 4 * 50 = 200 km away from Kolkata.

     

  8. Two trains running in opposite directions cross a man standing on the platform in 54 seconds and 32 seconds respectively and they cross each other in 44 seconds. Find the ratio of their speeds .
    4:7
    6:5
    9:7
    5:3
    7:5
    Option B
    Let the speeds of the two trains be x m/sec and y m/sec respectively.
    Then, length of the first train = 54x metres, and length of the second train = 32y metres.
    Therefore, (54x+32y)/(x+y) = 44
    =>54x – 44x = 44y – 32y
    => x/y = 6/5

     

  9. Two trains of equal length, running with the speeds of 40kmph and 60 kmph, take 40 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions ?
    8 sec.
    10 sec.
    12 sec.
    9 sec.
    6 sec.
    Option A
    Relative Speed = (60 -40) = 20 x 5/18 = 100/18
    Time = 40
    Distance = 40 x 100/18 = 2000/9
    Relative Speed = 60 + 40 = 100 x 5/18
    Time = (2000*18)/(9*500) = 8 sec.

     

  10. Two stations P and Q are 240 km apart on a straight line. One train starts from P at 4 p.m. and travels towards at 15 kmph. Another train starts from Q at 5 p.m. and travels towards P at a speed of 30 kmph. At what time will they meet?
    9 p.m.
    10 p.m.
    11 p.m.
    8 p.m.
    None of these
    Option C
    Let they meet x hours after 4 pm.
    Distance covered by P in x hours = 20x km.
    Distance covered by Q in (x – 1) hours = 25(x – 1) km.
    Therefore, 15x + 30(x – 1) = 240
    =>45x = 270
    => x = 6
    So, they meet at 10 p.m.

     


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