The total time taken by a boat to cover (D + 25) km downstream and the same…
2025
The total time taken by a boat to cover (D + 25) km downstream and the same distance upstream is 20 hours. Speed of boat in still water = 15 km/h. Speed of stream is 40% less than the boat’s speed. Find D.
- A.
66
- B.
71
- C.
78
- D.
62
Attempted by 11 students.
Show answer & explanation
Correct answer: B
Step 1: Given speeds. Boat in still water = 15 km/h. Stream speed is 40% less than the boat’s speed, so stream speed = 0.6 × 15 = 9 km/h.
Downstream speed = 15 + 9 = 24 km/h.
Upstream speed = 15 − 9 = 6 km/h.
Step 2: Set up the time equation. Let x = D + 25 be the distance each way. Total time = time downstream + time upstream = x/24 + x/6, and this equals 20 hours.
Combine fractions: x(1/24 + 1/6) = x(1/24 + 4/24) = x(5/24).
So x(5/24) = 20 ⇒ x = 20 × 24/5 = 96 km.
Step 3: Find D. D = x − 25 = 96 − 25 = 71 km.
Answer: 71 km.