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In the following question, two quantities I and II are given. Compare both quantities and choose the correct option. Quantity I: In a stream running at 2 km/h, a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water. Quantity II: A man can row 18 km/h in still water. It takes him thrice as long to row upstream as to row downstream. Find the rate of the stream.

1. Quantity I > Quantity II
2. Quantity I < Quantity II
3. Quantity I ≤ Quantity II
4. Quantity I ≥ Quantity II

Correct answer: Quantity I > Quantity II

Solution

For Quantity I, let the boat speed in still water be b. Then \(6/(b-2)+6/(b+2)=33/60\), which gives a value greater than the stream speed in Quantity II. For Quantity II, if upstream time is thrice downstream time, then \((18-s)/(18+s)=1/3\), giving stream speed 9 km/h. The first quantity is greater.

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