A boat travels 60 kilometers upstream in 3 hours and covers the same distance of 60 kilometers downstream in 2 hours. What is the speed of the boat in still water?
- (a)20 km/h
- (b)18 km/h
- (c)25 km/h
- (d)15 km/h
Answer
Why
Correct — C.
Rule: boat speed = (downstream + upstream) ÷ 2
Upstream speed: 60 ÷ 3 = 20 km/h
Downstream speed: 60 ÷ 2 = 30 km/h
Boat in still water: (30 + 20) ÷ 2
= 50 ÷ 2 = 25 km/h → option (c).
Why the others are wrong
- (a)20 km/h — 20 km/h is the upstream speed itself. Against the current the boat is slowed, so its still-water speed must be higher than 20.
- (b)18 km/h — 18 km/h is below even the upstream speed of 20 km/h. Still-water speed lies between the upstream and downstream speeds.
- (d)15 km/h — 15 km/h is half the downstream speed, 30 ÷ 2, with the upstream 20 left out. The boat speed averages both speeds.
Concept
Let the boat's speed in still water be b and the stream's be s. Downstream the current helps: speed = b + s. Upstream it opposes: speed = b − s.
Adding the two cancels s: 2b = downstream + upstream. Subtracting cancels b: 2s = downstream − upstream. So the boat speed is the average of the two, and the stream speed is half their difference.
Check: b = 25 and s = (30 − 20) ÷ 2 = 5 km/h. Then 25 − 5 = 20 km/h upstream covers 60 km in 3 hours, and 25 + 5 = 30 km/h downstream covers it in 2 hours.
Key facts
- Downstream speed = b + s, upstream speed = b − s.
- Boat speed = (downstream + upstream) ÷ 2.
- Stream speed = (downstream − upstream) ÷ 2, here 5 km/h.
Study next
Common traps
- Taking the upstream speed, 20 km/h, as the still-water speed
- Using the round-trip average speed, 120 km in 5 hours = 24 km/h, which is not the still-water speed
26 Sep 2025, 12:30, Reasoning Q.11 uses the difference formula instead: 4 km/h downstream and 3 km/h upstream give a stream speed of 0.5 km/h.
23 Sep 2024, 16:00, Quant Q.9 asks for the boat speed from 55 km in 5 hours and 11 hours: 11 and 5 km/h average to 8 km/h.
Related PYQs
No directly related past PYQ was found.