IBPS PO Quantitative Aptitude: Boats and Streams questions with solutions

Q1. A boat covers 28 km downstream and, while returning, covers only 75% of the downstream distance. If the boat takes 3 hours more to cover the upstream journey than the downstream journey, and the speed of the stream is \(5/9\) m/s, find the speed of the boat in still water.

1. 8 km/hr
2. 2 km/hr
3. 5 km/hr
4. 4 km/hr

Answer: 5 km/hr

The stream speed is \(5/9\) m/s = 2 km/h. Downstream distance is 28 km, and upstream distance is 75% of that, i.e. 21 km. Let the boat speed in still water be b; then downstream speed is b+2 and upstream speed is b-2, and the time difference equation gives b = 5 km/h.

Q2. A boat can travel at a speed of 13 km/h in still water. If the speed of the stream is 4 km/h, find the time taken by the boat to go 68 km downstream.

1. 2 hours
2. 3 hours
3. 4 hours
4. 5 hours

Answer: 4 hours

Downstream speed = 13 + 4 = 17 km/h. Time taken = distance/speed = 68/17 = 4 hours. So the correct answer is 4 hours.

Q3. A man's speed with the current is 15 km/h and the speed of the current is 2.5 km/h. The man's speed against the current is:

1. 8.5 km/h
2. 9 km/h
3. 10 km/h
4. 12.5 km/h

Answer: 10 km/h

Downstream speed = still-water speed + current speed. So still-water speed = 15 − 2.5 = 12.5 km/h. Upstream speed = 12.5 − 2.5 = 10 km/h.

Q4. 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 of the speed of the boat to the speed of the water current?

1. 2:1
2. 3:2
3. 8:3
4. Cannot be determined

Answer: 8:3

Upstream time is \(8\) h \(48\) min = \(44/5\) hours. Let boat speed be \(b\) and stream speed be \(s\). Since the same distance is covered, \(\frac{44}{5}(b-s)=4(b+s)\). Solving gives \(b:s=8:3\).

Q5. A motorboat, whose speed in still water is 15 km/h, goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/h) is:

1. 4
2. 5
3. 6
4. 10

Answer: 5

Let stream speed be \(x\) km/h. Then downstream speed is \(15+x\) and upstream speed is \(15-x\). Using total time \(4.5\) hours, \(\frac{30}{15+x}+\frac{30}{15-x}=4.5\), which gives \(x=5\).

Q6. In one hour, a boat goes 11 km/h along the stream and 5 km/h against the stream. The speed of the boat in still water (in km/h) is:

1. 3 km/h
2. 5 km/h
3. 8 km/h
4. 9 km/h

Answer: 8 km/h

Downstream speed is 11 km/h and upstream speed is 5 km/h. The speed in still water is the average of these two speeds: \((11+5)/2=8\) km/h. So the answer is 8 km/h.

Q7. A boat starts travelling from point Q then returns to point P. The boat takes 12 hours to complete the journey. The speed of the stream is 5 km/hour and the speed of the boat in still water is 10 km/hour. What is the distance between P and Q?

1. 25
2. 45
3. 30
4. 140

Answer: 45

Downstream speed = 15 km/hr. Upstream speed = 5 km/hr. Let distance P to Q = d. Time for both legs: d/15 + d/5 = 12. → d/15 + 3d/15 = 12 → 4d/15 = 12 → d = 45 km. Note: original source had '25' as answer (listed twice in options) which is incorrect. Correct answer is 45 km.

Q8. Ratio of speed of boat in down stream and speed of stream is 9:1, if speed of current is 3 km per hr, then find distance travelled(in km) upstream in 5 hours.

1. 105
2. 110
3. 120
4. 90

Answer: 105

Downstream:stream = 9:1. Stream = 3 km/hr → Downstream = 9×3 = 27 km/hr. Still water speed = downstream - stream = 27-3 = 24 km/hr. Upstream speed = still water - stream = 24-3 = 21 km/hr. Distance in 5 hours = 21×5 = 105 km. Note: original source had '90' as answer which is incorrect. Correct answer is 105.

Q9. Speed of boat in still water is 11.5 km/h. Speed of stream is 1.5 km/h. If it takes 4 hours to go downstream and return, what is the total distance traveled?

1. 520 km
2. 92 km
3. 184 km
4. 260 km

Answer: 520 km

Downstream = 13 km/hr, Upstream = 10 km/hr. Round trip: d/13 + d/10 = 4 → d(1/13+1/10) = 4 → d×23/130 = 4 → d = 520/23 ≈ 22.6 km. Total = 2d ≈ 45.2 km. The provided answer '520 km' is incorrect (likely computed as 13×10×4 = 520, wrong formula). None of the four options match the correct answer. Question is defective.

Q10. A boat has speed of 15 m/s in still water, but going upstream its speed is half the speed going downstream. The boat is going downstream and a ship (also going downstream) crosses the boat in 15 seconds. The ship is double the length of the boat and is 100 meters long. Find the time the ship will take to cover 144 km while going upstream.

1. 1 hour
2. 2 hours
3. 1.33 hours
4. 1.6 hours

Answer: 2 hours

Stream speed c: 15-c=(15+c)/2 → 30-2c=15+c → c=5 m/s. Boat downstream=20 m/s, upstream=10 m/s. Ship length=100m (boat=50m, half of ship). Ship crosses boat from behind (both downstream): relative speed=(100+50)/15=10 m/s. Ship downstream=boat downstream+relative=20+10=30 m/s. Ship still water=30-5=25 m/s. Ship upstream=25-5=20 m/s. Time=144×1000/20=7200 s=2 hours.

Q11. The total time taken by a boat to cover 105 km upstream and 105 km downstream is 7.5 hours. If the ratio of the speed of the boat in still water to the speed of the stream is 2:1, then find the speed of the boat in still water.

1. 44.5
2. 31.5
3. 43.5
4. 34.5

Answer: 31.5

The question as provided appears to contain an OCR or data inconsistency because the given options do not match the standard calculation from the stated ratio. In exam enrichment, the intended topic is boats and streams, and the keyed answer is retained from the source.

Q12. The ratio of the speed of a boat in still water to the speed of the current is 4:1. The total time taken by the boat to cover D km downstream and \(D-10\) km upstream is 12 hours. Find \(D\).

1. 125
2. 105
3. 80
4. Can't be determined

Answer: Can't be determined

Let the speed of current be \(c\), then still-water speed is \(4c\). Downstream speed = \(5c\) and upstream speed = \(3c\), so the time equation becomes \(\frac{D}{5c}+\frac{D-10}{3c}=12\), which contains both \(D\) and \(c\). Since there is only one equation for two unknowns, \(D\) cannot be uniquely determined.

Q13. If the sum of the upstream and downstream speeds is 36 km/h and the speed of the current is 3 km/h, then find the time taken to cover 52.5 km downstream.

1. 2 hr
2. 2.5 hr
3. 3 hr
4. 3.5 hr

Answer: 2.5 hr

If upstream speed is u and downstream speed is d, then u + d = 36 and d - u = 2×3 = 6. Solving gives d = 21 km/h. Time taken downstream = 52.5 ÷ 21 = 2.5 hours.