The upstream speed of a boat is 15 km/hr and the ratio of time taken by the…
2025
The upstream speed of a boat is 15 km/hr and the ratio of time taken by the boat to cover 105 km upstream and 108 km downstream 7 : 6 respectively. Find the speed of stream (in km/hr)?
- A.
1.5
- B.
5
- C.
4
- D.
7
- E.
1
Attempted by 4 students.
Show answer & explanation
Correct answer: A
Concept
For boats-and-streams problems, if b is the boat's speed in still water and s is the stream's speed, the upstream speed is b − s and the downstream speed is b + s. For a given leg, Speed = Distance ÷ Time, so knowing one leg's actual time (from its distance and speed) fixes the real time-scale for a stated time ratio between the two legs.
Application
Upstream speed is given: b − s = 15 km/hr.
Let the time for the upstream leg (105 km) be 7t and for the downstream leg (108 km) be 6t, matching the stated 7:6 ratio.
From the upstream leg, 105 ÷ (7t) = 15, which gives t = 1 hour, so the downstream leg takes 6t = 6 hours.
Downstream speed = 108 ÷ 6 = 18 km/hr, so b + s = 18.
Subtracting the two equations: (b + s) − (b − s) = 18 − 15 = 3 = 2s, so s = 1.5 km/hr.
Cross-check
With b = 16.5 km/hr and s = 1.5 km/hr: upstream speed = 16.5 − 1.5 = 15 km/hr (matches); downstream speed = 16.5 + 1.5 = 18 km/hr, giving upstream time 105/15 = 7 hours and downstream time 108/18 = 6 hours — a 7:6 ratio, exactly as stated.