Boats and Streams

Boats and Streams

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Aptitude miscellaneous
  1. Speed of a boat along and against the current are 14 kms/hr and 8 kms/hr respectively. The speed of the current is








  1. View Hint View Answer Discuss in Forum

    Given that , Rate downstream = 14 kmph
    Rate upstream = 8 kmph

    Speed of current =
    1
    		 (Rate downstream – Rate upstream)
    2

    Correct Option: D

    Given that , Rate downstream = 14 kmph
    Rate upstream = 8 kmph

    Speed of current =
    1
    		 (Rate downstream – Rate upstream)
    2

    Speed of current =
    1
    		 (14 – 8) kmph = 3 kmph
    2

  1. A motor boat covers a certain distance downstream in a river in 3 hours. It covers the same distance upstream in 3 hours and a half. If the speed of water is 1.5 km/h, then the speed of the boat in still water is :








  1. View Hint View Answer Discuss in Forum

    Let the speed of boat in still water be p kmph and the distance be q km.
    ∴ Rate downstream = (p + 1.5) kmph
    Rate upstream = (p – 1.5) kmph
    According to the question ,

    q
    		 = 3............(i)
    p + 1.5

    q
    		 =
    7
    		...........(ii)
    p - 152

    On dividing equation (i) by (ii),
    p - 1.5
    		 =
    3 × 2
    		 =
    6
    p + 1.577

    ⇒ 7p – 10.5 = 6p + 9
    ⇒ p = 10.5 + 9 = 19.5 kmph.
    We can find the required answer with the help of given formula :
    Here, t1 = 3.5, t2 = 3
    Speed of Stream = 1.5 km/hr
    Speed of Boat
    		 =
    t1 + t2
    Speed of Streamt1 - t2

    Correct Option: B

    Let the speed of boat in still water be p kmph and the distance be q km.
    ∴ Rate downstream = (p + 1.5) kmph
    Rate upstream = (p – 1.5) kmph
    According to the question ,

    q
    		 = 3............(i)
    p + 1.5

    q
    		 =
    7
    		...........(ii)
    p - 152

    On dividing equation (i) by (ii),
    p - 1.5
    		 =
    3 × 2
    		 =
    6
    p + 1.577

    ⇒ 7p – 10.5 = 6p + 9
    ⇒ p = 10.5 + 9 = 19.5 kmph.
    We can find the required answer with the help of given formula :
    Here, t1 = 3.5, t2 = 3
    Speed of Stream = 1.5 km/hr
    Speed of Boat
    		 =
    t1 + t2
    Speed of Streamt1 - t2

    Speed of Boat
    		 =
    3.5 + 3
    1.53.5 - 3

    Speed of Boat =
    6.5 × 1.5
    		 = 19.5 kmph
    0.5

  1. A man can row at 5 kmph. in still water. If the velocity of current is 1 kmph. and it takes him 1 hour to row to a place and come back, how far is the place?








  1. View Hint View Answer Discuss in Forum

    Let the distance be d km.
    Speed upstream = 5 – 1 = 4 kmph S
    peed downstream = 5 + 1 = 6 kmph

    ∴
    d
    		 +
    d
    		 = 1
    64

    ⇒
    2d + 3d
    		 = 1
    12

    ⇒ 5d = 12
    ⇒ d =
    12
    		 = 2.4 km
    5

    Second method to solve this question :
    Here, a = 5, b = 1
    Average Speed =
    (a + b)(a - b)
    a

    Correct Option: C

    Let the distance be d km.
    Speed upstream = 5 – 1 = 4 kmph S
    peed downstream = 5 + 1 = 6 kmph

    ∴
    d
    		 +
    d
    		 = 1
    64

    ⇒
    2d + 3d
    		 = 1
    12

    ⇒ 5d = 12
    ⇒ d =
    12
    		 = 2.4 km
    5

    Second method to solve this question :
    Here, a = 5, b = 1
    Average Speed =
    (a + b)(a - b)
    a

    Average Speed =
    (5 + 1)(5 - 1)
    5

    Average Speed =
    24
    		 = 4.8 kmph
    5

    Distance =
    1
    		 × 4.8 = 2.4 kmph
    2

  1. The speed of a motor-boat is that of the current of water as 36 : 5. The boat goes along with the current in 5 hours 10 minutes. It will come back in








  1. View Hint View Answer Discuss in Forum

    Let the speed of motor-boat be 36k kmph and and
    Speed of current = 5k kmph The boat goes along with the current in 5 hours 10 minutes i.e. 31/6 hours.
    As we know that , Distance = Time × Total speed

    Distance =
    31
    		 × (36k + 5k)
    6

    Distance =
    41k × 31
    		 km
    6

    Rate upstream = 36k – 5k = 31k kmph

    Correct Option: C

    Let the speed of motor-boat be 36k kmph and and
    Speed of current = 5k kmph The boat goes along with the current in 5 hours 10 minutes i.e. 31/6 hours.
    As we know that , Distance = Time × Total speed

    Distance =
    31
    		 × (36k + 5k)
    6

    Distance =
    41k × 31
    		 km
    6

    Rate upstream = 36k – 5k = 31k kmph
    ∴ Time taken =41k ×
    31
    6
    31k

    Time taken =
    41
    		hours or 6 hours 50 minutes
    6

  1. Two boats A and B start towards each other from two places, 108 km apart. Speed of the boat A and B in still water are 12km/hr and 15km/hr respectively. If A proceeds down and B up the stream, they will meet after.








  1. View Hint View Answer Discuss in Forum

    Let the speed of the stream be p kmph and both the boats meet after t hours
    Distance between two boats A and B = 108 km
    According to the question ,
    (12 + p) t + (15 – p ) t = 108
    ⇒ 12t + 15t = 108
    ⇒ 27t = 108

    Correct Option: B

    Let the speed of the stream be p kmph and both the boats meet after t hours
    Distance between two boats A and B = 108 km
    According to the question ,
    (12 + p) t + (15 – p ) t = 108
    ⇒ 12t + 15t = 108
    ⇒ 27t = 108

    ⇒ t =
    108
    		 = 4 hours
    27