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Boats and streams practice questions for bank exams
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Boats and streams is time, speed and distance with a moving river. A boat going downstream gets a push from the current, and a boat going upstream is held back. Questions give some of the speeds or times and ask for the others. Learn the two core relations below and the topic becomes a matter of reading the question carefully. Try the five questions at prelims pace.
Core relations
Let u be the boat's speed in still water and v the speed of the stream.
| Quantity | Formula |
|---|---|
| Downstream speed (D) | u + v |
| Upstream speed (U) | u − v |
| Speed in still water | u = (D + U) ÷ 2 |
| Speed of the stream | v = (D − U) ÷ 2 |
| Round trip over distance d | Time = d ÷ (u + v) + d ÷ (u − v) |
| Equal distance up and down | Times are in inverse ratio to the speeds |
Always work in the same units and use the effective speed (D or U) in distance ÷ speed.
Five practice questions
Question 1
The speed of a boat in still water is 12 km/h and the stream flows at 3 km/h. How long will the boat take to go 45 km downstream?
- A. 2.5 hours
- B. 3 hours
- C. 3.75 hours
- D. 5 hours
Question 2
A boat covers 20 km downstream in 2 hours and the same distance upstream in 4 hours. What is the speed of the boat in still water?
- A. 5 km/h
- B. 6 km/h
- C. 7.5 km/h
- D. 10 km/h
Question 3
A boat goes 30 km upstream and 44 km downstream in 10 hours. It also goes 40 km upstream and 55 km downstream in 13 hours. What is the speed of the boat in still water?
- A. 8 km/h
- B. 5 km/h
- C. 11 km/h
- D. 16 km/h
Question 4
A boat can travel at 5 km/h in still water, and the stream flows at 1 km/h. How long does it take to go 12 km downstream and return to the starting point?
- A. 3 hours
- B. 4 hours
- C. 4.5 hours
- D. 5 hours
Question 5
The ratio of a boat's downstream speed to its upstream speed is 5 : 3, and the stream flows at 4 km/h. What is the speed of the boat in still water?
- A. 20 km/h
- B. 16 km/h
- C. 12 km/h
- D. 8 km/h
Answers and explanations
- B. The downstream speed is 12 + 3 = 15 km/h, so the time is 45 ÷ 15 = 3 hours. The option 3.75 comes from wrongly using 12 km/h, and 5 comes from using 9 km/h.
- C. The downstream speed is 20 ÷ 2 = 10 km/h and the upstream speed is 20 ÷ 4 = 5 km/h. The still-water speed is (10 + 5) ÷ 2 = 7.5 km/h, and the stream is 2.5 km/h.
- A. Let 1/U = a and 1/D = b. The equations are 30a + 44b = 10 and 40a + 55b = 13. Multiply the first by 4 and the second by 3: 120a + 176b = 40 and 120a + 165b = 39. Subtract to get 11b = 1, so D = 11 km/h. Then 30a = 10 − 4 = 6, so U = 5 km/h. The still-water speed is (11 + 5) ÷ 2 = 8 km/h.
- D. Downstream the speed is 6 km/h, which takes 12 ÷ 6 = 2 hours. Upstream the speed is 4 km/h, which takes 12 ÷ 4 = 3 hours. The total is 5 hours.
- B. Let the speeds be 5k and 3k. The stream speed is (5k − 3k) ÷ 2 = k, so k = 4. The still-water speed is (5k + 3k) ÷ 2 = 4k = 16 km/h.
How to prepare boats and streams
- Compute D and U first. In every question, find downstream and upstream speeds as the first step, even when the question asks for something else.
- Memorise the half-sum and half-difference rules. They turn Questions 2 and 5 into one-line answers.
- Use reciprocals for paired equations. Treating 1/U and 1/D as unknowns, as in Question 3, gives a linear system that is quick to solve.
- Read the direction carefully. Many options are the right numbers with the wrong direction, such as the time upstream when the question asks for downstream.
- Link time and speed. If the distance is equal, speed and time are in inverse ratio, so a downstream time of 2 hours against an upstream time of 4 hours means speeds in the ratio 2 : 1.
- Practise the round-trip formula until you can write the total time in one line.
A realistic pace is 45 seconds for single-step questions and 90 seconds for the equation type. For the underlying relations, revisit time, speed and distance.
The full boats and streams topic test is on PrepMatic (about 15 questions, 30 minutes). The Quantitative Aptitude guide maps this topic against the rest of Quant, and the bank exam hub links each exam's pattern.
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