A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time. Find the speed of the boat in still water and the speed of the stream.

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.