The ratio of time taken by a boat to cover a distance in downstream to that of…
2023
The ratio of time taken by a boat to cover a distance in downstream to that of in upstream is 3 : 5. If the boat covers 90 km in downstream in t hours and 72 km in upstream in (t+1) hours, then find the downstream speed (in km/hr) of the boat.
Answer: D. 30 — Concept: For a fixed distance, time is inversely proportional to speed, so the ratio of times for the same distance gives the inverse ratio of speeds. Here…
- A.
20
- B.
36
- C.
24
- D.
30
- E.
18
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Correct answer: D
Concept: For a fixed distance, time is inversely proportional to speed, so the ratio of times for the same distance gives the inverse ratio of speeds. Here the downstream-to-upstream time ratio (for the same distance) is 3 : 5, which means the upstream-to-downstream speed ratio is 3 : 5.
Let upstream speed = 3k km/hr and downstream speed = 5k km/hr (speed ratio upstream : downstream = 3 : 5).
Downstream: 90 km is covered in t hours, so 90 = 5k x t, giving t = 18/k.
Upstream: 72 km is covered in (t+1) hours, so 72 = 3k x (t+1), giving t+1 = 24/k.
Subtract the time expressions: (t+1) - t = 24/k - 18/k, so 1 = 6/k, which gives k = 6.
Therefore downstream speed = 5k = 5 x 6 = 30 km/hr.
Cross-check: with k = 6, t = 18/6 = 3 hours and t+1 = 4 hours. Then downstream speed = 90/3 = 30 km/hr and upstream speed = 72/4 = 18 km/hr. For the same distance the time ratio is (1/30) : (1/18) = 3 : 5, matching the given condition.