A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along with the current in 10 minutes. How long will it take to go 6 km in stationary water?

Correct option is A

Given:

Distance traveled against the current = 2 km
Time taken against the current = 1 hour
Distance traveled along the current = 1 km
Time taken along the current = 10 minutes (converted to hours: 10/60 = 1/6 hours)
Formula Used:
Speed against the current: $$S_b - S_s = \frac{\text{Distance against current}}{\text{Time against current}}$$​​
Speed along the current:  $$S_b + S_s = \frac{\text{Distance along current}}{\text{Time along current}}$$​​
Speed in stationary water: $$S_b = \frac{(S_b + S_s) + (S_b - S_s)}{2}$$​​
Time to travel in stationary water:  $$T = \frac{\text{Distance}}{\text{Speed in stationary water}}$$​​
Solution:
• Speed against the current:
​$$S_b - S_s = \frac{2}{1} = 2 km/h$$​​
• Speed along the current:
​$$S_b + S_s = \frac{1}{1/6} = 6 km/h$$​​
• Speed in stationary water:
​$$S_b = \frac{6 + 2}{2} S_b = \frac{8}{2} S_b = 4 km/h$$​​
• Time required to travel 6 km in stationary water:
​$$T = \frac{6}{4} = 1.5 hours$$​​