Question

A boatman goes 84 km in the direction of current and then comes back in 10 hours Time taken to go 7 km in the direction of the current is equal to time taken to go 3 km against the direction of current Find the speed of the current. o 20 km/hr 12 km/hr 40 km/hr 8 km/h​

Answer 1

Answer:

Time taken to go 7 km in the direction of the current is equal to time taken to go 3 km against the direction of current.

Formula used:

Downstream speed = a + b

Upstream speed = a – b

Where,

a → Speed of a boat in still water

b → Speed of stream

Calculations:

Let the speed of boat in still water be 'a' and speed of stream be 'b'

So, speed of downstream = a + b

speed of upstream = a - b

According to the question

Time taken to go 7 km in the direction of the current is equal to time taken to go 3 km against the direction of current.

Time to cover 7 km in downstream = 7/(a + b)

Time to cover 3 km in upstream = 3/(a - b)

So, 7/(a + b) = 3/(a - b)

⇒ 7(a - b) = 3(a + b)

⇒ 7a - 7b = 3a + 3b

⇒ 7a - 3a = 7b + 3b

⇒ 4a = 10b

⇒ a/b = 5/2

Let the speed of boat in still water 5x and speed of stream be 2x

So, speed of downstream = 5x + 2x = 7x

speed of upstream = 5x - 2x = 3x

According to question,

⇒ 84/7x + 84/3x = 10

⇒ 12/x + 28/x = 10

⇒ 40/x = 10

⇒ x = 4

Speed of stream = 2x = 2 × 4 = 8 km/h

∴ Speed of stream is 8 km/h.