Question

Swati can row a boat on still water at a speed of 5 km/hr. However, on a given river, it takes her 1 hour more to row the boat 12 km upstream than downstream. One day, Swati rows the boat on this river from X to Y, which is N km upstream from X. Then she rows back to X immediately. If she takes at least 2 hours to complete this round trip, what is the minimum possible value of N?

• A. 3
• B. 4.8
• C. 2
• D. 3.6
• E. 2.1

Answer 1

The Correct Option is B

Let the speed of the stream be v km/hr. Then, - Speed upstream = (5 − v) km/hr - Speed downstream = (5 + v) km/hr

Step 1: Use the time difference condition 

Time taken upstream for 12 km = 12 / (5 − v) Time taken downstream for 12 km = 12 / (5 + v)

Given that upstream takes 1 hour more: 
12 / (5 − v) = 12 / (5 + v) + 1

Step 2: Solve for v

Simplify: 12 / (5 − v) − 12 / (5 + v) = 1 
12[(5 + v) − (5 − v)] / [(5 − v)(5 + v)] = 1 
12(2v) / (25 − v²) = 1 
24v = 25 − v² 
v² + 24v − 25 = 0

Solve quadratic: v = 1 (valid, since speed must be positive).

Step 3: Round trip condition

Effective speeds: - Upstream = 5 − 1 = 4 km/hr - Downstream = 5 + 1 = 6 km/hr

Time for N km upstream = N / 4 Time for N km downstream = N / 6 Total = N/4 + N/6 = (5N) / 12

Step 4: Apply total time condition

Total ≥ 2 hours: 
(5N)/12 ≥ 2 
5N ≥ 24 
N ≥ 24/5 = 4.8

Thus, the minimum possible value of N is 4.8 km.