Boats and Streams

“Boat and Stream problems test your ability to calculate effective speeds in flowing water. Common in SSC, Railways, and Banking exams.”

1. Basic Concepts and Formulas

Speed in still water = B km/hr
Stream speed = S km/hr
Downstream speed = B + S
Upstream speed = B - S
Time = Distance / Speed
Average speed (Round Trip) = (2 × Downstream × Upstream) / (Downstream + Upstream)

Type 1: Find Downstream and Upstream Speed
Example: Boat = 8 km/hr, Stream = 2 km/hr ⇒ Downstream = 10 km/hr, Upstream = 6 km/hr
Type 2: Find Speed of Boat in Still Water
Example: Downstream = 14 km/hr, Upstream = 6 km/hr ⇒ Boat = (14 + 6) / 2 = 10 km/hr
Type 3: Find Stream Speed
Example: Downstream = 14, Upstream = 6 ⇒ Stream = (14 – 6)/2 = 4 km/hr
Type 4: Time for Downstream and Upstream Journey
Example: Distance = 40 km, Downstream = 20, Upstream = 10 ⇒ Time = 2 + 4 = 6 hrs
Type 5: Average Speed for Round Trip
Example: Upstream = 12, Downstream = 18 ⇒ Avg speed = (2×12×18)/(12+18) = 14.4 km/hr
Type 6: Distance Calculation
Example: Time = 3 hr, Upstream = 6 ⇒ Distance = 6 × 3 = 18 km
Type 7: Boat takes less time downstream
Example: Downstream = 12, Upstream = 8, Distance = 48 ⇒ Time saved = 48/8 – 48/12 = 2 hrs

(SSC CGL 2022): A man rows 12 km downstream in 3 hours and returns upstream in 4 hours. Find speed of stream.
Solution: Downstream = 4 km/hr, Upstream = 3 km/hr ⇒ Stream = (4 – 3)/2 = 0.5 km/hr
(RRB NTPC 2020): A boat goes 30 km downstream in 3 hours and returns in 5 hours. Find boat speed in still water.
Solution: D = 30 ⇒ Downstream = 10, Upstream = 6 ⇒ Boat speed = (10 + 6)/2 = 8 km/hr
(SSC CHSL 2019): Downstream speed = 16 km/hr, Upstream speed = 12 km/hr. Find stream speed?
Solution: (16 – 12)/2 = 2 km/hr
(HSSC 2021): Boat travels 60 km downstream in 2 hrs, and upstream in 3 hrs. Find speed in still water.
Solution: D = 60 ⇒ Down = 30, Up = 20 ⇒ Boat speed = (30 + 20)/2 = 25 km/hr