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- Question
Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:
Options- A. 16 hours
- B. 18 hours
- C. 20 hours
- D. 24 hours
- Correct Answer
- 24 hours
ExplanationSpeed upstream = 7.5 kmph.Speed downstream = 10.5 kmph.
∴ Total time taken = ❨ 105 + 105 ❩hours = 24 hours. 7.5 10.5
Boats and Streams problems
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- 1. A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:
Options- A. 1 km/hr
- B. 1.5 km/hr
- C. 2 km/hr
- D. 2.5 km/hr Discuss
Correct Answer: 1 km/hr
Explanation:
Suppose he move 4 km downstream in x hours. Then,Speed downstream = ❨ 4 ❩ km/hr. x Speed upstream = ❨ 3 ❩ km/hr. x ∴ 48 + 48 = 14 or x = 1 . (4/x) (3/x) 2 So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.
Rate of the stream = 1 (8 - 6) km/hr = 1 km/hr. 2 - 2. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
Options- A. 40 minutes
- B. 1 hour
- C. 1 hr 15 min
- D. 1 hr 30 min Discuss
Correct Answer: 1 hr 15 min
Explanation:
Rate downstream = ❨ 1 x 60 ❩km/hr = 6 km/hr. 10 Rate upstream = 2 km/hr.
Speed in still water = 1 (6 + 2) km/hr = 4 km/hr. 2 ∴ Required time = ❨ 5 ❩hrs = 1 1 hrs = 1 hr 15 min. 4 4 - 3. The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is:
Options- A. 1.2 km
- B. 1.8 km
- C. 2.4 km
- D. 3.6 km Discuss
Correct Answer: 3.6 km
Explanation:
Speed downstream = (15 + 3) kmph = 18 kmph.Distance travelled = ❨ 18 x 12 ❩km = 3.6 km. 60 - 4. A boat covers a certain distance downstream in 1 hour, while it comes back in 1½ hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?
Options- A. 12 kmph
- B. 13 kmph
- C. 14 kmph
- D. 15 kmph
- E. None of these Discuss
Correct Answer: 15 kmph
Explanation:
Let the speed of the boat in still water be x kmph. Then,Speed downstream = (x + 3) kmph,
Speed upstream = (x - 3) kmph.
∴ (x + 3) x 1 = (x - 3) x 3 2 ⟹ 2x + 6 = 3x - 9
⟹ x = 15 kmph.
- 5. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:
Options- A. 2 mph
- B. 2.5 mph
- C. 3 mph
- D. 4 mph Discuss
Correct Answer: 2 mph
Explanation:
Let the speed of the stream x mph. Then,Speed downstream = (10 + x) mph,
Speed upstream = (10 - x) mph.
∴ 36 - 36 = 90 (10 - x) (10 + x) 60 ⟹ 72x x 60 = 90 (100 - x2)
⟹ x2 + 48x - 100 = 0
⟹ (x+ 50)(x - 2) = 0
⟹ x = 2 mph.
- 6. In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Options- A. 3 km/hr
- B. 5 km/hr
- C. 8 km/hr
- D. 9 km/hr Discuss
Correct Answer: 8 km/hr
Explanation:
Speed in still water = 1 (11 + 5) kmph = 8 kmph. 2 - 7. A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:
Options- A. 2 : 1
- B. 3 : 1
- C. 3 : 2
- D. 4 : 3 Discuss
Correct Answer: 3 : 1
Explanation:
Let man's rate upstream be x kmph.Then, his rate downstream = 2x kmph.
∴ (Speed in still water) : (Speed of stream) = ❨ 2x + x ❩ : ❨ 2x - x ❩ 2 2 = 3x : x 2 2 = 3 : 1.
- 8. A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
Options- A. 2 : 1
- B. 3 : 2
- C. 8 : 3
- D. Cannot be determined
- E. None of these Discuss
Correct Answer: 8 : 3
Explanation:
Let the man's rate upstream be x kmph and that downstream be y kmph.Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.
⟹ ❨ x x 8 4 ❩ = (y x 4) 5 ⟹ 44 x =4y 5 ⟹ y = 11 x. 5 ∴ Required ratio = ❨ y + x ❩ : ❨ y - x ❩ 2 2 = ❨ 16x x 1 ❩ : ❨ 6x x 1 ❩ 5 2 5 2 = 8 : 3 5 5 = 8 : 3.
- 9. A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.
Options- A. 2 hours
- B. 3 hours
- C. 4 hours
- D. 5 hours Discuss
Correct Answer: 4 hours
Explanation:
Speed downstream = (13 + 4) km/hr = 17 km/hr.Time taken to travel 68 km downstream = ❨ 68 ❩hrs = 4 hrs. 17 - 10.
If log a + log b = log (a + b), then: b a
Options- A. a + b = 1
- B. a - b = 1
- C. a = b
- D. a2 - b2 = 1 Discuss
Correct Answer: a + b = 1
Explanation:
log a + log b = log (a + b) b a ⟹ log (a + b) = log ❨ a x b ❩ = log 1. b a So, a + b = 1.
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