Quantitative Aptitude: Boats and Streams Questions Set 3

Boats and Streams Questions for IBPS PO, IBPS Clerk, IBPS RRB, SBI, LIC, IPPB, RBI and other exams. Boats and Streams Questions Bank PO.

1. A boat can cover 25 km upstream and 42 km downstream together in 7 hours. Also it can cover 30 km upstream and 63 km downstream together in 9 hours. What is the speed of the boat in still water?
   A) 13 km/hr
   B) 8 km/hr
   C) 7 km/hr
   D) 11 km/hr
   E) 16 km/hr
   
   View Answer

   Option A
   Solution:
   Upstream speed in both cases is 25 and 30 resp. Ratio is 25 : 30 = 5 : 6. So let times in both cases be 5x and 6x
   Downstream speed in both cases is 42 and 63 resp. Ratio is 42 : 63 = 2 : 3. So let times in both cases be 2y and 3y
   So 5x + 2y = 7
   and 6x + 3y = 9
   Solve both, x = 1, y = 1
   So upstream speed is = 25/5x = 5 km/hr
   And downstream = 42/2y = 21 km/hr
   So speed of boat is 1/2 * (5+21)
2. A man rows to a certain place and comes back, but by mistake he covers 1/3rd more distance while coming back. The total time for this journey is 10 hours. The ratio of speed of boat to that of stream is 2 : 1. If the difference between upstream and downstream speed is 12km/hr, then how much time will the man take to reach to starting point from his present position?
   A) 35 minutes
   B) 45 minutes
   C) 60 minutes
   D) 40 minutes
   E) 55 minutes
   
   View Answer

   Option D
   Solution:
   Speed of boat and stream – 2x and x respectively. So downstream speed = 2x+x = 3x, and upstream speed = 2x-x = x
   Let total distance between points is d km
   So he covered d km downstream, and while coming back i.e. upstream he covers d + 1/3 *d = 4d/3 km
   Total time for this journey is 10 hrs. So
   d/3x + (4d/3)/x = 10
   Solve, d = 6x
   Now also given, that (2x+x) – (2x-x) = 12
   Solve, x = 6
   So d = 36 km
   So to come to original point, he will have to cover 1/3 * 36 = 12 km
   And with speed 3x = 18 km/hr(downstream)
   So time is 12/18 * 60 = 40 minutes
3. A man can row at a speed of 15 km/hr in still water to a certain upstream point and back to the starting point in a river which flows at 9 km/hr. Find his average speed for total journey.
   A) 10.4 km/hr
   B) 8.4 km/hr
   C) 9.1 km/hr
   D) 5.2 km/hr
   E) 9.6 km/hr
   
   View Answer

   Option E
   Solution:
   When the distance is same, then average speed throughout journey would be:
   Speed downstream * Speed upstream/speed in still water.
   So here average speed = (15+9)*(15-9)/15 = 9.6 km/hr
4. A boat takes 5 hours for travelling downstream from point A to point B and coming back to point C at 3/4th of total distance between A and B from point B. If the velocity of the stream is 3 kmph and the speed of the boat in still water is 9 kmph, what is the distance between A and B?
   A) 24 km
   B) 32 km
   C) 27 km
   D) 21 km
   E) 34 km
   
   View Answer

   Option A
   Solution:
   Let total distance from A to B= d km, So CB = 3d/4 km
   So
   d/(9+3) + (3d/4)/(9-3) = 5
   Solve, d = 24 km
5. At its usual rowing rate, a boat can travel 18 km downstream in 4 hours less than it takes to travel the same distance upstream. But if he the usual rowing rate for his 28-km round trip was 2/3rd, the downstream 14 km would then take 12 hours less than the upstream 14 km. What is the speed of the current?
   A) 1.5 km/h
   B) 3 km/h
   C) 2 km/h
   D) 3.5 km/h
   E) 4 km/hr
   
   View Answer

   Option B
   Solution:
   Let speed of boat = x km/hr, and of current = y km/hr
   So
   18/(x-y) = 18/(x+y) + 4
   Gives x² = 9y + y²……..(1)
   Now when speed of boat is 2x/3
   14/(2x/3 -y) = 14/(2x/3 +y) + 12
   42/(2x-3y) = 42/(2x+3y) + 12
   Gives 4x² = 21y + 9y²…………(2)
   From (1), put value of x² in (2) and solve
   Solving, x = 6, y = 3
6. A boat can row to a place 120 km away and come back in 25 hours. The time to row 24 km with the stream is same as the time to row 16 km against the stream. Find the speed of current.
   A) 1.5 km/h
   B) 3 km/h
   C) 2 km/h
   D) 3.5 km/h
   E) 4 km/hr
   
   View Answer

   Option C
   Solution:
   Downstream speed = 24/x km/hr
   Upstream speed = 16/x km/hr
   120/(24/x) + 120/(16/x) = 25
   Solve, x = 2 km/hr
   So, downstream speed = 12 km/hr, upstream speed = 8 km/hr
   Speed of current = 1/2 * (12 – 8) km/hr
7. A boatman can row 4 Km along the stream in 20 minutes and return in 24 minutes. Find the speed of boatman in still water.
   A) 10 km/hr
   B) 8 km/hr
   C) 15 km/hr
   D) 12 km/hr
   E) 11 km/hr
   
   View Answer

   Option E
   Solution:
   Downstream speed = 4/20 * 60 = 12 km/hr
   Upstream speed = 4/24 * 60 = 10 km/hr
   Speed of boatman = 1/2 (12+10) = 11 km/hr
8. A man can row a certain distance downstream in 3 hours and return the same distance in 9 hours. If the speed of current is 18 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) 36 km/hr
   
   View Answer

   Option E
   Solution:
   Use formula:
   B = [t_u + t_d] / [t_u – t_d] * R
   B = [9+3] / [9-3] * 18
   B = 36 km/hr
9. Four times the downstream speed is 8 more than 15 times the upstream speed. If difference between downstream and upstream speed is 24 km/hr, then what is the ratio of speed in still water to the speed of the current?
   A) 9 : 2
   B) 5 : 3
   C) 7 : 1
   D) 4 : 1
   E) 7 : 3
   
   View Answer

   Option B
   Solution:
   Let speed in still water = x km/hr, of current = y km/hr
   So
   4 (x+y) = 15(x-y) + 8
   Solve, 11x – 19y + 8 = 0…….(1)
   Also (x+y) – (x-y) = 24
   So y = 12
   Put in (1). x = 20
   So x/y = 20/12 = 5/3
10. A boat can cover 14 km upstream and 21 km downstream together in 3 hours. Also it can cover 21 km upstream and 42 km downstream together in 5 hours. What is the speed of current?
    A) 13 km/hr
    B) 8 km/hr
    C) 7 km/hr
    D) 11 km/hr
    E) 16 km/hr
    
    View Answer

    Option C
    Solution:
    Upstream speed in both cases is 14 and 21 resp. Ratio is 14 : 21 = 2 : 3. So let times in both cases be 2x and 3x
    Downstream speed in both cases is 21 and 42 resp. Ratio is 21 : 42 = 1 : 2. So let times in both cases be y and 2y
    So 2x + y = 3
    and 3x + 2y = 5
    Solve both, x = 1, y = 1
    So upstream speed is = 14/2x = 7 km/hr
    And downstream = 21/y = 21 km/hr
    So speed of current is 1/2 * (21-7)