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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 chose the correct option. Quantity A: The ratio of speed of boat to speed of stream is 2 : 1, If the boat travels 162 km and come back to starting point in 36 hour. What is the difference between the time taken by the boat to go upstream and the time taken by the boat to go downstream? Quantity B: The speed of the stream is 6 km/hr and the distance travelled by the boat is 60 km. If the boat covered half distance upstream with usual speed and other half with double its speed, then it takes 7.5 hours less time than usual time to go upstream. Find the total time taken by the boat to go upstream and downstream?

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 chose the correct option. Quantity A: The ratio of speed of boat to speed of stream is 2 : 1, If the boat travels 162 km and come back to starting point in 36 hour. What is the difference between the time taken by the boat to go upstream and the time taken by the boat to go downstream? Quantity B: The speed of the stream is 6 km/hr and the distance travelled by the boat is 60 km. If the boat covered half distance upstream with usual speed and other half with double its speed, then it takes 7.5 hours less time than usual time to go upstream. Find the total time taken by the boat to go upstream and downstream? Correct Answer Quantity A < Quantity B

Quantity A:

Ratio of speed of boat to speed of stream = 2 : 1

Let Speed of Boat, SB = 2a and Speed of Stream, SS = a

TU + TD = Total time taken

⇒ Distance/ (Speed of boat downstream) + Distance/ (Speed of boat upstream) = Total Time taken

⇒ 162/ (2a + a) + 162/ (2a - a) = 36

⇒ 162 × = 36

⇒ (2a - a + 2a + a)/((2a + a) × (2a - a)) = 36/162

⇒ 4a/3a² = 2/9

⇒ 36a = 2 × 3a²

⇒ a = 6 km/hr

SS = 6 km/hr and SB 12 km/hr

Difference in time = 162/(12 - 6) - 162/(12 + 6) = 27 - 9 = 18 hours

Quantity B:

Let Speed of boat, SB = a km/hr

T - (TD + TU) = 7.5

⇒ 60/(a - 6) - 30/(a - 6) - 30/(2a - 6) = 7.5

⇒ 30/(a - 6) - 30/(2a - 6) = 7.5

⇒ 30 = 7.5

⇒ (2a - 6 - a + 6)/((a - 6)(2a - 6)) = 7.5/30

⇒ a/((a - 6)(2a - 6)) = 1/4

⇒ (a - 6)(2a - 6) = 4a

⇒ 2a² - 6a - 12a + 36 = 4a

⇒ 2a² - 22a + 36 = 0

⇒ a² - 11a + 18 = 0

⇒ a² - 2a - 9a + 18 = 0

⇒ a(a - 2) - 9(a - 2) = 0

⇒ (a - 2)(a - 9) = 0

⇒ a = 9 km/hr and 2 km/hr

Speed of boat is always greater than the speed of stream so, SB = 9 km/hr

Total time taken = 60/(9 + 6) + 60/(9 - 6) = 4 + 20 = 24 hours

∴ Quantity A < Quantity B

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