Answer :

Let the speed of the boat in still water and the speed of the stream be v kmph and u kmph respectively.


Speed of the boat in upstream direction = v - u


Speed of the boat in downstream direction = v + u


According to question -


12/(v - u) + 40/(v + u) = 8


12x + 40y = 8 [ Let 1/(v - u) = x and 1/(v + u) = y ]


3x + 10y = 2 .....(1)


and,


16/(v - u) + 32/(v + u) = 8


16x + 32y = 8 [Let 1/(v - u) = x and 1/(v + u) = y]


2x + 4y = 1.....(2)


From equation (1), we get -


x = (2 - 10y)/3.....(3)


Substituting the value of x in equation (2), we get -




4 - 8y = 3


8y = 1


y = 1/8


v + u = 8.....(4)


substituting the value of y in equation (3), we get -


x = 1/4


v - u = 4.....(5)


Adding equations (4) and (5), we get -


v = 6


Substituting the value of v in equation (4), we get -


u = 2


Thus, Speed of the boat in still water = 6 kmph and speed of stream = 2 kmph.


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