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Boat & Stream Test 182
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Boat & Stream Test 182

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  • Question 1/5
    1 / -0
    The ratio of the speed of the boat downstream and speed of boat is 3 : 2, If 120km distance travelled upstream in 30 hours then find the speed of the boat?
    Solutions
    D=S+R, U=S-R
    Then,
    S+R/S=3/2
    2(S+R)=3S
    2R=S----(1)
    Upstream,
    Distance/S-R=time
    120/S-R=30
    S-R=4
    S=4+R-----(2)
    From equation 1 and 2,
    2R=4+R
    R=4km/h
    Then,
    2R=S
    2*4=S
    S=8km/h
    Hence, option D.
  • Question 2/5
    1 / -0

    Vinay can row a certain distance upstream in 9 hours and return to the same distance 3 hours early. If the stream flows at a rate of 3 km/hr, find the speed of Vinay in still water.

    Solutions

    Given, Vinay can row a certain upstream in 9h and return the same distance 3 hours early.
    Let the speed of Vinay in still water be ‘a’ km/hr
    Speed of stream is 3 km/hr
    Relative speed of Vinay going upstream = a – 3 km/hr
    Relative speed of Vinay going downstream = a + 3 km/hr
    Time = distance/speed
    ⇒ 9 = distance/(a – 3) ------ (1) and 6 = distance/(a + 3) ------ (2)
    Dividing (1) by (2)
    ⇒ 3/2 = (a + 3)/(a – 3)
    ⇒ 3a – 9 = 2a + 6
    ⇒ a = 15 km/hr

  • Question 3/5
    1 / -0
    Sujan can swim up to a certain distance upstream in 5 hours and returns to the origin in 2 hours. The speed of the stream is 5 km/hr. Find the time required to cover 25 km upstream by him.
    Solutions
    Let the swimming speed of Sujan in still water be x km/hr.
    The speed of the stream is 5 km/hr.
    So, Sujan’s speed in upstream = (x – 5) km/hr.
    Sujan’s speed in downstream = (x + 5) km/hr.
    Sujan can swim up to a certain distance upstream in 5 hours and returns to the origin in 2 hours.
    So, the distance travelled in upstream = (x – 5) × 5 km.
    And, the distance travelled in downstream = (x + 5) × 2 km.
    Now, we can write,
    (x – 5) × 5 = (x + 5) × 2
    ⇒ 5x – 25 = 2x + 10
    ⇒ 3x = 35
    ⇒ x = 35/3
    So, the swimming speed of Sujan in still water = 35/3 km/hr.
    Then, the speed of Sujan in upstream = (35/3) – 5 km/hr.
    = 20/3 km/hr.
    ∴ The time required to cover 25 km upstream by him = 25/(20/3) = 15/4 hrs.
    = 3 hours and 45 minutes.
  • Question 4/5
    1 / -0
    King of Saudi Arabia is a boats enthusiast. Aquaholic is a boat designed for him. During one of his adventures, his boat took twice the time to travel upstream than it took to travel the same distance downstream. If the speed of boat in still water is, 50kmph then find the speed of boat downstream.
    Solutions
    Let the speed of stream be x
    Speed of boat upstream = 50 – x
    Speed of boat downstream = 50 + x
    Let the distance travelled be Y
    Then,
    2Y/(50+x) = Y/(50 – x)
    2/(50 + x) = 1(50 – x)
    50 + x = 2(50 – x)
    50 + x = 100 – 2x
    3x = 50
    x = 50/3=16.66 
    Speed of stream = 16.66kmph
    Speed of boat downstream = 66.66kmph
  • Question 5/5
    1 / -0
    A boat takes a total of 9 hours 36 minutes to cover 180 km in upstream and 180 km in downstream. If sum of upstream speed of boat and downstream speed of boat is 80 km/hr, then find the speed of current.
    Solutions

    Let speed of boat in still water be x km/hr and speed of current be y km/hr

    Using the data provided in the question, we get:

    (x + y) + (x – y) = 80

    ⇒ x = 40 km/hr

     9.6

    ⇒ y = 10 km/hr

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