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In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: A boat takes 6 hrs. 40 min. to travel 60 km upstream and return back. If the speed of the stream is 3.75 km/hr, find the downstream speed. Quantity B: A boat takes 12 min. to travel 4.1 km in still water. When the speed of the stream is 4 km/hr, find the downstream speed.

In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: A boat takes 6 hrs. 40 min. to travel 60 km upstream and return back. If the speed of the stream is 3.75 km/hr, find the downstream speed. Quantity B: A boat takes 12 min. to travel 4.1 km in still water. When the speed of the stream is 4 km/hr, find the downstream speed. Correct Answer Quantity A < Quantity B

Solving for Quantity A:

Let the downstream speed and upstream speed be ‘a’ km/hr and ‘b’ km/hr respectively

As we know, downstream speed - upstream speed = 2(speed of stream)

⇒ a - b = 2(3.75) = 7.5

⇒ b = a - 7.5 ---- (1)

Also,

Time taken downstream + time taken upstream = total time taken

⇒ 60/a + 60/b = 6 + 40/60

⇒ 1/a + 1/b = (20/3)/60 = 1/9

⇒ 9(a + b) = ab

Substituting for ‘b’ from (1),

⇒ 9a + 9(a - 7.5) = a(a - 7.5)

⇒ 18a - 67.5 = a2 - 7.5a

⇒ a2 - 25.5a + 67.5 = 0

⇒ a2 - 3a - 22.5a + 67.5 = 0

⇒ (a - 3)(a - 22.5) = 0

⇒ a = 3, 22.5

⇒ b = -4.5, 15

But, speed cannot be negative, hence, a = 22.5 km/hr

⇒ Quantity A = 22.5 km/hr

Solving for Quantity B:

Speed of boat in still water = 4.1/(12/60) = 20.5 km/hr

Speed of stream = 4 km/hr

Downstream speed = speed in still water + speed of stream = 20.5 + 4 = 24.5 km/hr

⇒ Quantity B = 24.5 km/hr

∴ Quantity A < Quantity B

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