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- Question
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
- Correct Answer
- 8 km/hr
ExplanationSpeed in still water = 1 (11 + 5) kmph = 8 kmph. 2
Boats and Streams problems
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- 1. 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 Discuss
Correct Answer: 24 hours
Explanation:
Speed upstream = 7.5 kmph.Speed downstream = 10.5 kmph.
∴ Total time taken = ❨ 105 + 105 ❩hours = 24 hours. 7.5 10.5 - 2. 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 - 3. 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 - 4. 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 - 5. 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.
- 6. 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.
- 7. 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.
- 8. 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 - 9.
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.
- 10. If ax = by, then:
Options- A.
log a = x b y - B.
log a = x log b y - C.
log a = y log b x - D. None of these Discuss
Correct Answer:log a = y log b x
Explanation:
ax = by⟹ log ax = log by
⟹ x log a = y log b
⟹ log a = y . log b x
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