Quantitative Aptitude: Time, Speed and Distance Set 2

  1. A train overtakes two persons who are walking at the rate of 8 kmph and 12 kmph in the same direction in which the train is going, and passes them completely in 9 and 10 seconds respectively. What is the length of the train?
    A) 200 m
    B) 500 m
    C) 100 m
    D) 300 m
    E) None of these
    View Answer
    Option C
    Solution:

    length of the train = (Difference in speeds * Product of time) / Difference in Time
    S1 = 8 * 5/18 = 20/9 m/s
    S2 = 12 * 5/18 = 30/9 m/s
    length of the train = (10/9)* 9 *10 /1 = 100m

  2. Two trains A and B start from Delhi and Chennai towards Chennai and Delhi respectively. After passing each other they take 19 hours 30 minutes and 8 hours 40 minutes to reach Chennai and Delhi respectively. If the train from Delhi is moving at 80 km/hr then find the speed of the train from Chennai?
    A) 110 kmph
    B) 100 kmph
    C) 90 kmph
    D) 120 kmph
    E) None of these
    View Answer
    Option D
    Solution:

    Speed of train B = Speed of train A * Square root of (t1/t2)
    Speed of train B = 80 * Square root of ((39/2)/26/3)
    Speed of train B = 80 * 3/2 = 120 kmph
  3. From Stations P and Q, two trains start moving towards each other at the speeds of 120 kmph and 80 kmph respectively. When the two trains meet each other, it is found that one train has covered 80 km more than that of another train. Find the distance between the stations P and Q?
    A) 145 km
    B) 400 km
    C) 200 km
    D) 180 km
    E) None of these
    View Answer
    Option B
    Solution:

    Distance between Stations P and Q = [Relative Speed]/Difference of Speed * d
    Distance = (200/40) * 80 = 400 km
  4. Two trains leave Chennai for Delhi at 9 pm and 9:45 pm respectively and travel at 80 kmph and 120 kmph respectively. How many km from Chennai, will the two trains meet?
    A) 180 km
    B) 130 km
    C) 140 km
    D) 160 km
    E) None of these
    View Answer
    Option A
    Solution:

    Distance = Difference in time *[Product of speeds / Difference in speeds]
    Distance = 45/60 * [(80*120)/40] = 180 km
  5. The distance between two stations A and B is 280 km. One train at a speed of 80 kmph leaves station A at 6:00 pm towards station B. Another train at a speed of 120 kmph leaves station B at 7:00 pm towards station A. Then at what time both trains meet?
    A) 10:00 pm
    B) 9:00 pm
    C) 11:00 pm
    D) 8:00 pm
    E) None of these
    View Answer
    Option D
    Solution:

    First train speed = a ; Second train speed = b
    Time taken to meet = (Distance (+/-) t(b))/Relative Speed
    If the second train started after the first train then [+t]
    Time taken to meet = (Distance + t(b))/Relative Speed
    Time taken to meet = (280 + 1(120))/200 = 2h
    Time both trains meet at = 6.00 pm + 2h = 8:00 pm
  6. The distance between two stations A and B is 280 km. One train at a speed of 80 kmph leaves station A at 7:00 pm towards station B. Another train at a speed of 120 kmph leaves station B at 6:00 pm towards station A. Then at what time both trains meet?
    A) 6:50 pm
    B) 7:48 pm
    C) 10:40 pm
    D) 9:20 pm
    E) None of these
    View Answer
    Option B
    Solution:

    First train speed = a ; Second train speed = b
    Time taken to meet = (Distance (+/-) t(b))/Relative Speed
    If the second train started before the first train then [-t]
    Time taken to meet = (Distance – t(b))/Relative Speed
    Time taken to meet = (280 – 1(120))/200 = 48 minutes
    Time both trains meet at = 7.00 pm + 48 minutes = 7:48 pm
  7. The distance between two stations P and Q is 250 km. A train leaves P towards Q at 80 kmph. After half an hour another train leaves Q towards P at 120 kmph. Find the distance of the point where the two trains meet, from P.
    A) 132 km
    B) 145 km
    C) 128 km
    D) 124 km
    E) None of these
    View Answer
    Option D
    Solution:

    The distance of the point where the two trains meet is “x”
    x/80 – (250 – x)/120 = 1/2
    3x – 2(250 – x) =1/2 * 240
    3x – 500 + 2x = 120
    5x = 620
    x = 124 km.
  8. The distance between two stations P and Q is 240 km A train starts from P towards Q and another train from Q to P at the same time and they meet after 8 hours. The train travel traveling from P to Q is slower by 6 kmph compared to another train from B to A, then find the speed of the slower train?
    A) 12 kmph
    B) 15 kmph
    C) 20 kmph
    D) 13 kmph
    E) None of these
    View Answer
    Option A
    Solution:

    Speed of slower train = x
    Speed of faster train = x+6
    Relative speed = 2x + 6
    240/2x + 6 = 8
    240 = 16x – 48
    16x = 192
    x = 12 kmph
  9. A train covers the distance between P and Q in 4 hours. If the speed is reduced by 4 kmph, then the same distance is covered in 5 hours. Find the speed of the train in Kmph?
    A) 10 kmph
    B) 15 kmph
    C) 25 kmph
    D) 18 kmph
    E) 20 kmph
    View Answer
    Option E
    Solution:

    d/x = 4
    d/x-4 = 5
    4x = 5x – 20
    x = 20 kmph
  10. A train covers the distance between P and Q in 5 hours. If the speed is reduced by 5 kmph, then the same distance is covered in 6 hours. Find the reduced speed and distance between P and Q in km?
    A) 10 kmph; 100 km
    B) 15 kmph; 120 km
    C) 30 kmph; 150 km
    D) 18 kmph; 120 km
    E) 25 kmph; 150 km
    View Answer
    Option E
    Solution:

    d/x = 5
    d/x-5 = 6
    5x = 6x – 30
    x = 30 kmph
    Reduced speed = x -5 = 30 – 5 = 25 kmph
    d = 150

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