Boats and Streams problems
- 1. A man can row three-quarters of a kilometre against the stream in 11¼ minutes and down the stream in 7½ minutes. The speed (in km/hr) of the man in still water is:
Options- A. 2
- B. 3
- C. 4
- D. 5 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Analyst, Bank Clerk, Bank PO
Correct Answer: 5
Explanation:
We can write three-quarters of a kilometre as 750 metres,
and 11¼ minutes as 675 seconds.
| Rate upstream = | ❨ | 750 | ❩m/sec | = | 10 | m/sec. |
| 675 | 9 |
| Rate downstream = | ❨ | 750 | ❩m/sec | = | 5 | m/sec. |
| 450 | 3 |
| ∴ Rate in still water = | 1 | ❨ | 10 | + | 5 | ❩m/sec |
| 2 | 9 | 3 |
| = | 25 | m/sec |
| 18 |
| = | ❨ | 25 | x | 18 | ❩km/hr |
| 18 | 5 |
= 5 km/hr.
- 2. A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:
Options- A. 8.5 km/hr
- B. 9 km/hr
- C. 10 km/hr
- D. 12.5 km/hr Discuss
Correct Answer: 10 km/hr
Explanation:
Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.
Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.
- 3. A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
Options- A. 2.4 km
- B. 2.5 km
- C. 3 km
- D. 3.6 km Discuss
Correct Answer: 2.4 km
Explanation:
Speed downstream = (5 + 1) kmph = 6 kmph.
Speed upstream = (5 - 1) kmph = 4 kmph.
Let the required distance be x km.
| Then, | x | + | x | = 1 |
| 6 | 4 |
⟹ 2x + 3x = 12
⟹ 5x = 12
⟹ x = 2.4 km.
- 4. A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?
Options- A. 4 km/hr
- B. 6 km/hr
- C. 8 km/hr
- D. Data inadequate Discuss
Correct Answer: 6 km/hr
Explanation:
| Rate downstream = | ❨ | 16 | ❩kmph = 8 kmph. |
| 2 |
| Rate upstream = | ❨ | 16 | ❩kmph = 4 kmph. |
| 4 |
| ∴ Speed in still water = | 1 | (8 + 4) kmph = 6 kmph. |
| 2 |
- 5. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
Options- A. 4
- B. 5
- C. 6
- D. 10 Also asked in: Bank Exams
Correct Answer: 5
Explanation:
Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr.
| ∴ | 30 | + | 30 | = 4 | 1 |
| (15 + x) | (15 - x) | 2 |
| ⟹ | 900 | = | 9 |
| 225 - x2 | 2 |
⟹ 9x2 = 225
⟹ x2 = 25
⟹ x = 5 km/hr.
- 6. 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.
- 7. 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.
- 8. 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 |
- 9. 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 |
- 10. 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 |
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