A boat goes 12 km

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.