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The time taken by a ship to travel 1000 km upstream is 40 hours more than the time taken by it to travel the same distance in downstream. The speed of the ship in still water is 200% more than that of the speed of stream. Quantity I: How much time the ship will take to travel the same distance in upstream?  Quantity II: How much time the ship will take to travel 2000 km downstream if due to wind, the speed of stream was increased by 50%?

The time taken by a ship to travel 1000 km upstream is 40 hours more than the time taken by it to travel the same distance in downstream. The speed of the ship in still water is 200% more than that of the speed of stream. Quantity I: How much time the ship will take to travel the same distance in upstream?  Quantity II: How much time the ship will take to travel 2000 km downstream if due to wind, the speed of stream was increased by 50%? Correct Answer Quantity 1 > Quantity 2

Given:

Distance travelled = 1000 km

Time taken to travel upstream = 40 hours + time taken to travel downstream

Speed of wind = 50% more

Calculations:

Let the speed of the stream = X km per hour

⇒ The speed of the ship in still water = (100 + 200)% of X

⇒ 300% of X

⇒ 3 × X km per hour

According to the question,

⇒ (1000/(3X – X)) – (1000/(3X + X)) = 40

⇒ (1000/2X) – (1000/4X) = 40

⇒ 1000 × 2 = 8X × 40

⇒ X = 6.25 km/hr

Quantity I :

The required time = 1000/(3X – X)

⇒ 1000/2X

⇒ 1000/(2 × 6.25)

∴ required time = 80 hours

⇒ New speed of stream = 1.5x 

Quantity II :

W hen the speed of stream was increased by 50% then the new speed of the stream = 150% of x

⇒ New speed of stream = 1.5 × 6.25

⇒ New speed of stream = 9.375 km/hr

⇒ The speed of the ship in downstream = 3x + x = 4x, where x = new speed of stream 

⇒ 9.375 × 4 = 37.5 km/hr

⇒ The required time = 2000/37.5 ≈ 53 hours

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