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In river A, the distance travelled by a boat downstream in time T is 50% more than the distance travelled by the same boat upstream in the same time. In river B, the same boat travels a distance of 11 km upstream in 30 minutes. If the speed of the current in river B is 2 km/h, what is the speed of the stream in river A? (The speed of the boat in still water is same in both the rivers)

In river A, the distance travelled by a boat downstream in time T is 50% more than the distance travelled by the same boat upstream in the same time. In river B, the same boat travels a distance of 11 km upstream in 30 minutes. If the speed of the current in river B is 2 km/h, what is the speed of the stream in river A? (The speed of the boat in still water is same in both the rivers) Correct Answer None of these

Given:

In river A, the distance travelled by a boat downstream in time T is 50% more than the distance travelled by the same boat upstream in the same time

Let the distance travel by boat upstream = 2 units

∴ Distance travel by boat downstream = 3 units

Calculation:

Let the speed of the boat be x

Speed of the stream in river A be y

According to first case

Distance = speed × time

⇒ (x + y) × T = 3  ----(i)

⇒ (x - y) × T = 2  ----(ii)

By second case of river B

Speed of stream = 2 km/hr

Speed of the boat = x

Distance covered upstream = 11 kms

Time taken to cover the distance = 30 mins = (1/2) hrs

Distance = speed × time

⇒ 11 = (x - 2) × (1/2)

⇒ 22 = x - 2

⇒ 24 = x

∴ Speed of the boat = 24 km/hr

Putting the value of x in equation (i) and (ii) and dividing equation (i) and (ii)

⇒ {(24 + y) / (24 - y)} = (3/2)

⇒ 48 + 2y = 72 - 3y

⇒ 5y = 24

⇒ y = 4.8 km/hr

∴ Speed of the boat = 4.8 km/hr

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