Quants Questions : Time and Distance Set 8 – Boats

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1. A boat can travel 4.2km upstream in 14min. If the ratio of the speed of the boat in still water to the speed of the stream is 7:1. How much time will the boat take to cover 17.6km downstream ?
   A)56min
   B)44min
   C)32min
   D)48min
   E)None of these
   
   Answer

   B)44min
   Explanation :
   Speed = 7x:x
   Downstream = 8x; upstream = 6x
   Upstream speed = 4.2*60/14 = 18kmph
   6x = 18
   X = 3
   Downstream = 8*3 = 24
   Time taken for 17.6km = 17.6*60/24 = 44min
   
   
   
2.  A man can row at 4 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back. how far is that place.
   A)1.8km
   B)2.6km
   C)1.5km
   D)3.2km
   E)None of these
   
   Answer

   A)1.8km
   Explanation :
   Let the distance is x km
   Rate downstream = 4 + 1 = 5 kmph
   Rate upstream = 4 – 1 = 3 kmph
   then
   x/5 + x/3 = 1
   3x + 5x = 15
   x = 15/8 = 1.8 km
   
   
   
3. Arun  takes thrice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat in still water and stream is
   A)3:1
   B)1:2
   C)2:1
   D)2:3
   E)None of these
   
   Answer

   C)2:1
   Explanation :
   speed downstream = x kmph
   Speed upstream = 3x kmph
   (3x+x)/2 : (3x-x)/2
   4x/2 : 2x/2 = 2:1
   
   
   
4. A boat takes 30 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 2 kmph and the speed of the boat in still water is 15 kmph, what is the distance between A and B?
   A)342km
   B)356km
   C)316km
   D)308km
   E)None of these
   
   Answer

   D)308km
   Explanation :
   velocity of the stream = 2 kmph
   Speed of the boat in still water is 15 kmph
   Speed downstream = (15+2) = 17 kmph
   Speed upstream = (15-2) = 13 kmph
   Let the distance between A and B be x km
   x/17+(x/2)/13=30
   x/17+x/26=30
   43x/442=30
   x=30*442/43 = 308.37 = 308km
   distance between A and B = 308 km
   
   
   
5. A boat takes 120min less to travel 30km downstream than to travel the same distance upstream.If the speed of the boat in still water is 8kmph then the speed of the stream is
   A)2kmph
   B)8kmph
   C)3kmph
   D)4kmph
   E)None of these
   
   Answer

   A)2kmph
   Explanation :
   Speed of the stream = x
   (30/8-x) – (30/8+x)= 120/60 = 2/1
   30(8+x) – 30(8-x) = 2[64 – x²]
   240+30x-240x+30x = 2[64 – x²]
   60x = 128- 2x²
   2x²+60x-128 = 0
   x²+30x-64 = 0
   (x+32)(x-2) = 0
   X=2kmph
   
   
   
6. A boat running downstream covers a distance of 24km in 4hrs, while for covering
   the same distance upstream it takes 6hrs, what is the speed of the boat in still water ?
   A)12kmph
   B)10kmph
   C)5kmph
   D)7kmph
   E)None of these
   
   Answer

   C)5kmph
   Explanation :
   24/x-y = 6
   6x – 6y = 24………….(1)
   24/x+y = 4
   4x+4y = 24………….(2)
   24x – 24y = 96
   24x+24y = 144
   Solve abv 2 equ
   48x = 240
   X = 240/48 = 5
   
   
   
7. A man swims downstream 40 km in 5 hours and upstream 24 km in 2 hours. Find his speed in still water ?
   A)10kmph
   B)15kmph
   C)8kmph
   D)12kmph
   E)None of these
   
   Answer

   A)10kmph
   Explanation :
   Downstream  = 40/5= 8 kmph
   Upstream = 24/2== 12 kmph
   Speed in still water = 1/2 ( 8+12) = 10 kmph
   
   
   
8. The speed of a boat in still water in 12 km/hr and the rate of current is 4 km/hr. The
   distance travelled downstream in 12 minutes is
   A)3.2km
   B)4.7km
   C)5.1km
   D)2.7km
   E)None of these
   
   Answer

   A)3.2km
   Explanation :
   Speed downstream = (12 + 4) kmph = 16 kmph.
   Distance travelled = 16 x12/60 km = 3.2 km
   
   
   
9. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
   A)1.30hrs
   B)3.209hrs
   C)2.15hrs
   D)1.25hrs
   E)None of these
   
   Answer

   D)1.25hrs
   Explanation :
   downstream =(1x 60)/10  = 6 kmph
   Rate upstream = 2 km/hr.
   Speed in still water =(6 + 2) /2= 4 kmph
   time = 5/4 =  1.25hrs
   
   
   
10. A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30km upstream and 21 km downstream in 6 hours and 30 minutes. The speed of the boat in still water is 
    A)10kmph
    B)4kmph
    C)6kmph
    D)8kmph
    E)None of these
    
    Answer

    A)10kmph
    Explanation :
    speed of the boat in still water = x kmph
    speed of the current = y kmph
    upstream speed = (x – y) kmph
    downstream speed = (x + y)kmph
    24/(x-y) + 28/(x+y) = 6
    30/(x-y) + 21(x+y) = 13/2
    X = 10kmph
    
    
    

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