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- Question
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
- 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.
- 1. 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
Options- A. 10
- B. 13
- C. 14
- D. 15 Discuss
- 2. A man completes 5⁄8 of a job in 10 days. At this rate, how many more days will it takes him to finish the job?
Options- A. 5
- B. 6
- C. 7
- D. 7 1⁄2 Discuss
- 3. A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
Options- A. 29 1⁄5
- B. 37 1⁄4
- C. 42
- D. 54 Discuss
- 4. If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?
Options- A. 48 paise
- B. 54 paise
- C. 56 paise
- D. 72 paise Discuss
- 5. Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
Options- A. 648
- B. 1800
- C. 2700
- D. 10800 Discuss
- 6. 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
- 7. 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
- 8. 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
- 9. 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 Discuss
- 10. 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
Boats and Streams problems
Search Results
Correct Answer: 13
Explanation:
Let the required number of days be x
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
| Persons | 30 | : | 39 | ] | :: 12 : x |
| Working hours/day | 6 | : | 5 |
∴ 30 x 6 x x = 39 x 5 x 12
| ⟹ x = | (39 x 5 x 12) |
| (30 x 6) |
⟹ x = 13.
Correct Answer: 6
Explanation:
| Work done = | 5 |
| 8 |
| Balance work = | ❨ | 1 - | 5 | ❩ | = | 3 |
| 8 | 8 |
Let the required number of days be x.
| Then, | 5 | : | 3 | = :: 10 : x | ⟺ | 5 | x x = | 3 | x 10 |
| 8 | 8 | 8 | 8 |
| ⟹ x = | ❨ | 3 | x 10 x | 8 | ❩ |
| 8 | 5 |
⟹ x = 6.
Correct Answer: 42
Explanation:
After 10 days : 150 men had food for 35 days.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
∴ 125 : 150 :: 35 : x ⟺ 125 x x = 150 x 35
| ⟹ x = | 150 x 35 |
| 125 |
⟹ x = 42.
Correct Answer: 48 paise
Explanation:
Let the required weight be x kg.
Less weight, Less cost (Direct Proportion)
∴ 250 : 200 :: 60 : x ⟺ 250 x x = (200 x 60)
| ⟹ x= | (200 x 60) |
| 250 |
⟹ x = 48.
Correct Answer: 1800
Explanation:
Let the required number of bottles be x
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
| Machines | 6 | : | 10 | ] | :: 270 : x |
| Time (in minutes) | 1 | : | 4 |
∴ 6 x 1 x x = 10 x 4 x 270
| ⟹ x = | (10 x 4 x 270) |
| (6) |
⟹ x = 1800.
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.
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.
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 |
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.
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.
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