MathematicsA motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours, Find the speed of the boat in still water and the speed of the stream.

A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours, Find the speed of the boat in still water and the speed of the stream.


  1. A
    speed of boat = 6km/h and speed of stream = 10km/h
  2. B
    speed of boat = 5km/h and speed of stream = 2km/h   
  3. C
    speed of boat = 2km/h and speed of stream = 5km/h  
  4. D
    speed of boat = 10km/h and speed of stream = 4km/h 

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    Solution:

    Given that a motor boat can travel 30 km upstream and 28 km downstream in 7 hours and it can travel 21 km upstream and return in 5 hours. We need to find the speed of the boat in still water and the speed of the stream.
    A system of linear equations a 1 x+ b 1 y+ c 1 =0   and a 2 x+ b 2 y+ c 2 =0  , cross multiplication method is given as:
    x b 1 × c 2 b 2 × c 1 = y c 1 × a 2 c 2 × a 1 = 1 a 1 × b 2 a 2 × b 1  
     We will form a pair of linear equations and solve them by using cross-multiplication method.
    Let speed of boat in still water be x km/h and speed of stream be y km/h.
    Time taken to cover 30 km upstream is 30 xy  .
    Time taken to cover 28 km downstream is 28 x+y  .
    Time taken to cover 21 km upstream is 21 xy  .
    Time taken to cover 21 km downstream is 21 x+y  .
    According to the question, we have,
    28 x+y + 30 xy =7 21 x+y + 21 xy =5  
    Let us assume p= 1 x+y   and q= 1 xy  , then we have,
    28p+30q7=0 21p+2h5=0  
    Now solving these equations by cross multiplication we have,
    p (30)(5)(21)(7) = q (7)(21)(5)(28) = 1 (28)(21)(2)(30) p 150+147 = q 47+40 = 1 588630 p 3 = q 7 = 1 42  
    On comparing we have,
    p 3 = 1 42 42p=3 p= 3 42 p= 1 14  
    Similarly, we have,
    q 7 = 1 42 42q=7 q= 7 42 q= 1 6  
    From here we have,
    1 x+y = 1 14 x+y=14...(i)  
    1 xy = 1 6 xy=6...(ii)  
    Now, adding equation (i) and (ii), we have,
    2x=20 x= 20 2 x=10  
    Now substituting the value of x in equation (ii), we have,
    10y=6  
    y=106 y=4  
    Hence the speed of stream and that of the boat in still water are 4 km/h and 10 km/h respectively.
    Therefore, option 1 is correct.
     
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