Boats and Streams
- A man 8 km/hr in still water. If the river is running at 2 km/hr, it taken 32 minutes to row to a place and back. How for is the place ?
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D/(8 - 2) + D/(8 + 2) = 32/60
Correct Option: C
∵ D/(8 - 2) + D/(8 + 2) = 32/60
⇒ D/6 + D/10 = 32/60
⇒ 10D + 6D = 32
∴ D = 2 km
- A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream in 61/2 hours. The velocity of the current is ?
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Let the speed upstream be U km/hr and the speed downstream be V km/hr respectively.
Then 24/U + 36/V = 6 ...(i)
and 36/U + 24/V = 13/2 ...(ii)Correct Option: C
Let the speed upstream be U km/hr and the speed downstream be V km/hr respectively.
Then 24/U + 36/V = 6 ...(i)
and 36/U + 24/V = 13/2 ...(ii)
Solving these 2 equations we get
∴ U = 8 km/hr and V = 12 km/hr
∴ Velocity of current = (12 - 8)/2 km/hr = 2 km/hr
- A boat goes at 14 kmph along the stream and 8 kmph against the stream. The speed of the boat (in kmph) in still water is :
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Given in question , Rate downstream = 14 kmph
Rate upstream = 8 kmphSpeed of boat in still water = 1 (Rate downstream + Rate upstream) 2
Correct Option: B
Given in question , Rate downstream = 14 kmph
Rate upstream = 8 kmphSpeed of boat in still water = 1 (Rate downstream + Rate upstream) 2 Speed of boat in still water = 1 (14 + 8) = 11 kmph 2
- A man goes downstream with a boat to some destination and returns upstream to his original place in 5 hours. If the speed of the boat in still water and the stream are 10 km/hr and 4 km/ hr respectively, the distance of the destination from the starting place is
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Let the distance of the destination from the starting point be d km.
Rate downstream = (10 + 4) kmph = 14 kmph
Rate upstream = (10 – 4) kmph = 6 kmph
According to the question,d + d = 5 14 6 ⇒ 3d + 7d = 5 42
⇒ 10d = 42 × 5⇒ d = 42 × 5 = 21 km 10
We can find the required answer with the help of given formula :
Here, p = 10, q = 4, t = 5d = t(p² - q²) 2p
Correct Option: C
Let the distance of the destination from the starting point be d km.
Rate downstream = (10 + 4) kmph = 14 kmph
Rate upstream = (10 – 4) kmph = 6 kmph
According to the question,d + d = 5 14 6 ⇒ 3d + 7d = 5 42
⇒ 10d = 42 × 5⇒ d = 42 × 5 = 21 km 10
We can find the required answer with the help of given formula :
Here, p = 10, q = 4, t = 5d = t(p² - q²) 2p d = 5(10² - 4²) 2 × 10 d = 5(100 - 16) 2 × 10 d = 84 = 21 4
- In a fixed time, a boy swims double the distance along the current that he swims against the current. If the speed of the current is 3 km/hr, the speed of the boy in still water is
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Let the rate of swimming in still water be p kmph
∴ Rate down-stream = (p + 3) kmph
∴ Rate up-stream = (p – 3) kmph
According to the question,
(p + 3) t = 2 (p – 3) × t
⇒ p + 3 = 2p – 6
⇒ p = 9 kmph
Using the given formula :
Here, t1 = 2k , t2 = k
Speed of Stream = 3 km/hr∴ Speed of Boy = t1 + t2 Speed of Stream t1 - t2
Correct Option: B
Let the rate of swimming in still water be p kmph
∴ Rate down-stream = (p + 3) kmph
∴ Rate up-stream = (p – 3) kmph
According to the question,
(p + 3) t = 2 (p – 3) × t
⇒ p + 3 = 2p – 6
⇒ p = 9 kmph
Using the given formula :
Here, t1 = 2k , t2 = k
Speed of Stream = 3 km/hr∴ Speed of Boy = t1 + t2 Speed of Stream t1 - t2 Speed of Boy = 2k + k 3 2k - k
Speed of Boy = 9 km/hr