Each question contains Quantity I and Quantity II. Read the information carefully and answer accordingly. Quantity I: Vipin can swim at 6 km/h in still water. The river flows at 3 km/h, and it takes him 8 hours more to swim upstream than downstream for the same distance. How far is the place (one way)? Quantity II: A man can row at 25 km/h in still water and the river runs at 15 km/h. If he takes 2 hours to row to a place and back, how far is that place (one way)?

Introduction / Context:
This problem is a comparative question involving two separate time and distance situations with boats or swimmers in running water. We are required to compute the one-way distance in each scenario and then compare the two quantities. It tests the concepts of upstream and downstream speeds, the use of time differences, and the average time for a round trip on a river. These ideas appear frequently in aptitude exams under “boats and streams” or “swimming in a river” topics.

Given Data / Assumptions:
- Quantity I: Swimming speed of Vipin in still water = 6 km/h.
- River flow speed = 3 km/h.
- It takes 8 hours more to swim upstream than downstream for the same distance.
- Quantity II: Rowing speed in still water = 25 km/h.
- River flow speed = 15 km/h.
- Total time for rowing to a place and back = 2 hours.
- All speeds are constant and the river flows uniformly in a straight path in both cases.

Concept / Approach:
For motion in a river, the effective upstream speed is (still water speed - stream speed), and the downstream speed is (still water speed + stream speed). Time is distance divided by speed. For Quantity I, we set up an equation using the given time difference between upstream and downstream journeys. For Quantity II, we use the total round-trip time to find the one-way distance. After compute both distances, we compare them to decide which quantity is greater.

Step-by-Step Solution:
Quantity I:Upstream speed = 6 - 3 = 3 km/h.Downstream speed = 6 + 3 = 9 km/h.Let the one-way distance be d km.Time upstream = d / 3 hours; time downstream = d / 9 hours.Given that upstream time is 8 hours more: d / 3 - d / 9 = 8.Compute: (1/3 - 1/9) * d = (2/9) * d = 8, so d = 8 * 9 / 2 = 36 km.Quantity II:Downstream speed = 25 + 15 = 40 km/h.Upstream speed = 25 - 15 = 10 km/h.Let one-way distance be x km.Total time: x / 40 + x / 10 = 2.Compute: (1/40 + 1/10) * x = (1/40 + 4/40) * x = (5/40) * x = x / 8 = 2, so x = 16 km.

Verification / Alternative check:
Recheck both distances. For Quantity I: upstream time = 36 / 3 = 12 hours; downstream time = 36 / 9 = 4 hours; difference = 8 hours, which matches the condition. For Quantity II: downstream time = 16 / 40 = 0.4 hours; upstream time = 16 / 10 = 1.6 hours; total = 2 hours, which again matches. Therefore, Quantity I is 36 km and Quantity II is 16 km, making Quantity I clearly larger.

Why Other Options Are Wrong:
- Quantity I = Quantity II would require both distances to be equal, but 36 km is not equal to 16 km.
- Quantity I < Quantity II is incorrect because 36 is greater than 16, not smaller.
- “Relationship cannot be determined” is wrong because the data in both quantities is sufficient to determine unique distances and compare them directly.

Common Pitfalls:
Some candidates mistakenly use still-water speeds instead of upstream or downstream speeds or mix up which is which. Others may mis-handle the time difference equation in Quantity I or the total time equation in Quantity II. It is also common to think that the comparison is tricky and that it cannot be determined, but as the calculations show, both distances are clearly defined. Always convert verbal statements about “more time” or “round-trip time” into explicit equations before comparing quantities.

Final Answer:
Quantity I is greater than Quantity II.