Tuesday, December 17, 2024
Banking QuizQuant

Quantitative Aptitude: Boats and Streams Set 2

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  1. A boat can cover 21 km in the direction of current and 15 km against the current in 3 hours each. Find the speed of current.
    A) 4.5 km/hr
    B) 2.5 km/hr
    C) 3 km/hr
    D) 1 km/hr
    E) 6 km/hr
    View Answer
    Option D
    Solution:
    Downstream speed = 21/3 = 7 km/hr
    Upstream speed = 15/3 = 5 km/hr
    So speed of current = 1/2 * (7-5)
  2. A boat in a river with speed of stream as 6 km/hr can travel 7 km upstream and back in 4 hours. What is the speed of the boat in still water?
    A) 10 km/hr
    B) 8 km/hr
    C) 11 km/hr
    D) 12 km/hr
    E) 15 km/hr
    View Answer
    Option B
    Solution:
    Let speed of boat is x km/hr
    So
    7/(x+6) + 7/(x-6) = 4
    Solve, x = 8 km/hr [ignore the negative root because speed cannot be negative]
  3. A boat can cover 40 km upstream and 60 km downstream together in 13 hours. Also it can cover 50 km upstream and 72 km downstream together in 16 hours. What is the speed of the boat in still water?
    A) 5.5 km/hr
    B) 6.5 km/hr
    C) 8.5 km/hr
    D) 3.5 km/hr
    E) None of these
    View Answer
    Option C
    Solution:
    Upstream speed in both cases is 40 and 50. Ratio is 40 : 50 = 4 : 5. So let times in both cases be 4x and 5x
    Downstream speed in both cases is 60 and 72 resp. Ratio is 60 : 72 = 5 : 6. So let times in both cases be 5y and 6y
    So 4x + 5y = 13
    and 5x + 6y = 16
    Solve both, x = 2, y = 1
    So upstream speed is = 40/4x = 5 km/hr
    And downstream = 60/5y = 12 km/hr
    So speed of boat is 1/2 * (5+12)
  4. A boat can row to a place 56 km away and come back in 22 hours. The time to row 21 km with the stream is same as the time to row 12 km against the stream. Find the speed of boat in still water.
    A) 1.5 kmph
    B) 3.5 kmph
    C) 5.5 kmph
    D) 7.5 kmph
    E) None of these
    View Answer
    Option C
    Solution:
    Downstream speed = 21/x km/hr
    Upstream speed = 12/x km/hr
    56/(21/x) + 56/(12/x) = 22
    Solve, x = 3 km/hr
    So, downstream speed = 7 km/hr, upstream speed = 4 km/hr
    Speed of boat = 1/2 * (7 + 4) km/hr
  5. A boat travels downstream from point A to B and comes back to point C half distance between A and B in 18 hours. If speed of boat is still water is 7 km/hr and distance AB = 80 km, then find the downstream speed.
    A) 15 km/hr
    B) 18 km/hr
    C) 12 km/hr
    D) 10 km/hr
    E) 6 km/r
    View Answer
    Option D
    Solution:
    A to B is 80, so B to is 80/2 = 40 km
    Let speed of current = x km/hr
    So 80/(7+x) + 40/(7-x) = 18
    Solve, x = 3 km/hr
    So downstream speed = 7 + 3 = 10 km/hr
  6. A boat can cover 20 km upstream and 32 km downstream together in 3 hours. Also it can cover 40 km upstream and 48 km downstream together in 5 and half hours. What is the speed of the current?
    A) 13 km/hr
    B) 8 km/hr
    C) 7 km/hr
    D) 11 km/hr
    E) 16 km/hr
    View Answer
    Option D
    Solution:
    Upstream speed in both cases is 20 and 20 resp. Ratio is 20 : 40 = 1 : 2. So let times in both cases be x and 2x
    Downstream speed in both cases is 32 and 48 resp. Ratio is 32 : 48 = 2 : 3. So let times in both cases be 2y and 3y
    So x + 2y = 3
    and 2x + 3y = 5 1/2
    Solve both, x = 2, y = 0.5
    So upstream speed is = 20/x = 10 km/hr
    And downstream = 32/2y = 32 km/hr
    So speed of boat is 1/2 * (32-10)
  7. Speed of boat in still water is 14 km/hr while the speed of current is 10 km/hr. If it takes a total of 7 hours to row to a place and come back, then how far is the place?
    A) 30 km
    B) 18 km
    C) 24 km
    D) 32 km
    E) None of these
    View Answer
    Option C
    Solution:
    USE FORMULA:
    Distance = total time * [B2 – R2]/2*B
    So distance = 7 * [142 – 102]/2*14
    Distance = 24 km
  8. A man can row a certain distance downstream in 4 hours and return the same distance in 8 hours. If the speed of current is 16 km/hr, find the speed of man in still water.
    A) 47 km/hr
    B) 48 km/hr
    C) 42 km/hr
    D) 50 km/hr
    E) None of these
    View Answer
    Option B
    Solution:
    Use formula:
    B = [tu + td] / [tu – td] * R
    B = [8+4] / [8-4] * 16
    B = 48 km/hr
  9. There are 3 point A, B and C in a straight line such that point B is equidistant from points A and C. A boat can travel from point A to C downstream in 12 hours and from B to A upstream in 8 hours. Find the ratio of boat in still water to speed of stream.
    A) 9 : 2
    B) 8 : 3
    C) 7 : 1
    D) 4 : 1
    E) 7 : 3
    View Answer
    Option C
    Solution:
    Let speed in still water = x km/hr, of current = y km/hr
    Downstream speed = (x+y) km/hr
    Upstream speed = (x – y) km/hr
    Let AC = 2p km. So AB = BC = p km.
    So
    2p/(x+y) = 12
    And
    p/(x-y) = 8
    Divide both equations, and solve
    x/y = 7/1
  10. A boat can row 18 km downstream and back in 8 hours. If the speed of boat is increased to twice its previous speed, it can row same distance downstream and back in 3.2 hours. Find the speed of boat in still water.
    A) 9 km/hr
    B) 5 km/hr
    C) 4 km/hr
    D) 8 km/hr
    E) 6 km/hr
    View Answer
    Option E
    Solution:
    Let speed of boat = x km/hr and that of stream = y km/hr
    So
    18/(x+y) + 18/(x-y) = 8
    when speed of boat becomes 2x km/hr:
    18/(2x+y) + 18/(2x-y) = 3.2
    Solve, x= 6 km/hr

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