Aptitude Questions : Time and Distance Set 12 – Boats

Hello Aspirants. Welcome to Online Quantitative Aptitude Section in AffairsCloud.com. Here we are creating question sample in Time and Distance – Boats and streams with Explanation, which is common for all the IBPS, SBI, SSC and other competitive exams. We have included Some questions that are repeatedly asked in bank exams !!!

1. A boat can travel 15 km downstream in 18 min. The ratio of the speed of the boat in still water to the speed of the stream is 4 : 1. How much time will the boat take to cover 10 km upstream?
   A) 22 min
   B) 25 min
   C) 20 min
   D) 33 min
   E) 30 min
   
   Answer & Explanation

   C) 20 min
   Explanation:
   Use:
   B = [t_u + t_d] / [t_u – t_d] * R
   15 km downstream in 18 min so 10 km in (18/15)*10 = 12 min
   B= 4x, R = x
   Now
   4x = [t_u + 12] / [t_u – 12] * x
   Solve, t_u = 20 min
   
   
   
2. Speed of a man in still water is 4 km/hr and the river is running at 2 km/hr. The total time taken to go to a place and come back is 4 hours. What is the distance travelled?
   A) 16 km
   B) 13 km
   C) 10 km
   D) 6 km
   E) 8 km
   
   Answer & Explanation

   D) 6 km
   Explanation:
   Use
   Distance = time * [B^2 – R^2] / 2*B
   Distance = 4* [4^2 –2^2] / 2*4
   
   
   
3. A boat takes 25 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 5 km/hr and the speed of the boat in still water is 10 km/hr, what is the distance between A and B?
   A) 100 km
   B) 122 km
   C) 146 km
   D) 178 km
   E) 150 km
   
   Answer & Explanation

   E) 150 km
   Explanation:
   Downstream speed = 10+5 = 15
   Upstream speed = 10-5 = 5
   Now total time is 25 hours
   If distance between A and B is d, then distance BC = d/2
   Now distance/speed = time, so
   d/15 + (d/2)/5= 25
   Solve, d = 150 km
   
   
4. A boat goes 6 km against the current of the stream in 2 hours and goes 8 km along the current in half hour. How long will it take to go 28.5 km in stationary water?
   A) 4 1/2 hours
   B) 3 hours
   C) 3 1/2 hours
   D) 4 hours
   E) None of these
   
   Answer & Explanation

   B) 3 hours
   Explanation:
   Speed upstream = 6/2 = 3, speed downstream = 8/(1/2) = 16
   Speed of boat = 1/2(3+16) = 9.5 km/hr
   So time in still water = 28.5/9.5
   
   
5. A man can row 48 km upstream and 56 km downstream in 12 hrs. Also, he can row 54 km upstream and 70 km downstream in 14 hrs. What is the speed of man in still water?
   A) 4 km/hr
   B) 10 km/hr
   C) 12 km/hr
   D) 15 km/hr
   E) 18 km/hr
   
   Answer & Explanation

   B) 10 km/hr
   Explanation:
   Let upstream speed = x km/hr, downstream speed = y km/hr
   So 48/x + 56/y = 12
   And 54/x + 70/y = 14
   Put 1/x = u, 1/y = v
   So equations are 48u + 56v = 12 and 54u + 70v = 14
   Solve the equations, u = 1/6, v = 1/14
   So upstream speed = 6 km/hr, downstream speed = 14 km/hr
   Speed of boat in still water = 1/2*(6+14)
   
   
   
6. A boat takes 150 min less to travel 40 km downstream than to travel the same distance upstream. The speed of the stream is 4 km/hr. What is the downstream speed?
   A) 16 km/hr
   B) 12 km/hr
   C) 10 km/hr
   D) 8 km/hr
   E) None of these
   
   Answer & Explanation

   A) 16 km/hr
   Explanation:
   Let speed of boat in still water = x km/hr
   So speed upstream = x-4, and speed downstream = x+4
   Now given:
   Time to travel 40 km downstream = time to travel 40 km upstream – 150/60
   So 40/(x+4) = 40/(x-4) – 5/2
   8/(x-4) – 8/(x+4) = 1/2
   x+4 – (x-4)/(x² – 16) = 1/16
   solve, x = 12
   so downstream speed = 12+4
   
   
7. A man rows to a place 40 km distant and back in a total of 18 hours. He finds that he can row 5 km with the stream in the same time as 4 km against the stream. What is the speed of boat in still water?
   A) 4.5 km/hr
   B) 8 km/hr
   C) 5.5 km/hr
   D) 2 km/hr
   E) None of these
   
   Answer & Explanation

   A) 4.5 km/hr
   Explanation:
   Suppose he moves 5km downstream in x hours
   Then, downstream speed a= 5/x km/hr
   Speed upstream speed b = 4/x km/hr
   40 / (5 /x) + 40 / (4/x) = 18
   8x + 10x = 18
   x = 1
   a = 5 km/hr, b = 4 km/hr
   speed of boat = ½ (5 + 4 ) = 9/2 km/hr
   
   
   
8. In a stream running at 2 km/hr, a motorboat goes 6 km upstream and back again to the starting point in 2 hours. Find the speed of boat in still water.
   A) 9 km/hr
   B) 12 km/hr
   C) 8 km/hr
   D) 10 km/hr
   E) None of these
   
   Answer & Explanation

   C) 8 km/hr
   Explanation:
   Distance = time * [B^2 – R^2] / 2*B
   6 = 2 * [B^2 – 4^2] / 2*B
   B^2 – 6B – 16 = 0
   (B-8)(B+2) = 0
   So B = 8
   
   
9. It takes five times as long to row a distance against the stream as to row the same distance in favor of the stream. What is the ratio of the speed of the boat in still water to that of stream?
   A) 7 : 4
   B) 2 : 3
   C) 9 : 5
   D) 3 : 2
   E) 5 : 2
   
   Answer & Explanation

   D) 3 : 2
   Explanation:
   Use:
   B = [t_u + t_d] / [t_u – t_d] * R
   So
   B =[5x + x] / [5x- x] * R
   So B/R = 6/4 = 3/2
   
   
   
10. A boat running downstream covers a distance of 32 km in 4 hrs and for covering the same distance upstream it takes 8 hrs. What is the speed of the stream?
    A) 5 km/hr
    B) 2 km/hr
    C) 6 km/hr
    D 4 km/hr
    E) 3 km/hr
    
    Answer & Explanation

    B) 2 km/hr
    Explanation:
    Downstream speed = 32/4 = 8 km/hr
    Upstream speed = 32/8 = 4 km/hr
    So speed of stream = 1/2*(8-4)