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Boats & Streams Questions and Answers

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1.

A man can row a boat to reach a place upstream in 10 minutes. He took only 5 minutes to return downstream. If the speed of the stream is 2 m/s, then the speed of the boat is:

Exam Year(s)

DSSSB PGT - 2023,

Answer: D

The distance is the same both ways, so the speeds are inversely proportional to the times. Upstream takes 10 minutes and downstream 5 minutes, so the downstream speed is twice the upstream speed. With the boat's speed b and the stream's speed 2 m/s, the equation is as shown.

\[ b + 2 = 2(b - 2) \]

\[ b = 6 \]

The speed of the boat in still water is 6 m/s. Check: upstream 4 m/s and downstream 8 m/s, which is double.

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2.

The speed of stream is 4 km/hr. A boat goes 120 km and comes back to the starting point in 40 hours. What is the speed of the boat in still water?

Exam Year(s)

DSSSB - 2023,

Answer: B

Let the speed of the boat in still water be v km/hr. Going down the stream the speed is v + 4 and coming back it is v - 4, and the total time is 40 hours.

\[ \frac{120}{v+4} + \frac{120}{v-4} = 40 \]

\[ \frac{240v}{v^{2}-16} = 40 \Rightarrow v^{2} - 6v - 16 = 0 \]

This gives v = 8, so the speed in still water is 8 km/hr, option (B). Speeds of 15 and 10 would take much less than 40 hours. Check: 120 / 12 = 10 hours downstream and 120 / 4 = 30 hours upstream, and 10 + 30 = 40 hours, which agrees with the given time.

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3.

The time taken by a boat to go 21 km downstream is equal to the time taken by it to go 9 km upstream. To go 12 km downstream and the same distance upstream, it takes a total of \(5\frac{5}{7}\) hours. How much time (in hours) will the boat take to go 28 km downstream?

Exam Year(s)

DSSSB TGT - 2023,

Answer: C

The boat takes 4 hours to go 28 km downstream. Equal times for 21 km downstream and 9 km upstream mean the speeds are in the ratio 21 : 9 = 7 : 3, so downstream speed is \(7k\) and upstream speed is \(3k\). \[ \begin{aligned} \frac{12}{7k} + \frac{12}{3k} &= 5\frac{5}{7} \\ &= \frac{40}{7} \end{aligned} \] \[ \begin{aligned} \frac{12 + 28}{7k} &= \frac{40}{7k} \\ &= \frac{40}{7} \Rightarrow k \\ &= 1 \end{aligned} \] Downstream speed is 7 km/h, so \[ \frac{28}{7} = 4\text{ hours} \] The other options do not match this speed.

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4.

A man can row 40 km upstream and 55 km downstream in 13 hours. Also, he can row 30 km upstream and 44 km downstream in 10 hours. Then the speed of the man in still water and the speed of the current is:

Exam Year(s)

HPPSC HPAS - 2021,

Answer: A

The man rows at 8 km/h in still water and the current is 3 km/h: (8, 3 kmph).

Let the upstream speed be u and the downstream speed d. Write a = 1/u and b = 1/d to make the equations linear.

\[ \begin{aligned} 40a + 55b &= 13 \\ 30a + 44b &= 10 \end{aligned} \]

\[ \begin{aligned} 120a + 165b &= 39 \\ 120a + 176b &= 40 \\ 11b &= 1,\ b = \tfrac{1}{11} \end{aligned} \]

Then \(40a = 13 - 5 = 8\), so a = 1/5. The speeds are u = 5 km/h and d = 11 km/h.

\[ \begin{aligned} \text{still water} &= \tfrac{11 + 5}{2} = 8 \\ \text{current} &= \tfrac{11 - 5}{2} = 3 \end{aligned} \]

All options give 8 for the boat, so only the current differs; 4, 3.2 and 3.5 km/h do not satisfy both trips.

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5.

A woman takes 1/11 time in rowing a certain distance downstream than upstream. What is the ratio of the speed of the current to the speed of the boat in still water?

Exam Year(s)

Haryana Civil Services - 2026, HPSC - 2026,

Answer: D

The ratio of the speed of the current to the speed of the boat is 5/6.

Read as the key does, the downstream trip takes 1/11 of the upstream time over the same distance, so the speeds are in the inverse ratio. Let b be the speed in still water and c the current.

\[ \begin{aligned} \frac{b - c}{b + c} &= \frac{1}{11} \\ 11b - 11c &= b + c \\ 10b &= 12c \Rightarrow \frac{c}{b} = \frac{5}{6} \end{aligned} \]

6/5 is the same ratio upside down (boat to current). 11/5 and 11/6 come from mixing the 11 into the answer instead of solving for it.

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6.

Which of the following statements is/are correct?

1. 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 will be 10 km/hr.
2. The speed of a boat in still water is 22 km/hr. and the rate of current flow is 3 km/hr. The distance travelled in downstream direction in 12 minutes will be 5 km.

Select the answer using the code given below:

Exam Year(s)

Haryana Civil Services - 2026, HPSC - 2026,

Answer: C

Both 1 and 2 are correct.

Statement 1: speed with the current = man + current, so the man's own speed is \(15 - 2.5 = 12.5\) km/h, and against the current he makes \(12.5 - 2.5 = 10\) km/h. True.

Statement 2: downstream speed is \(22 + 3 = 25\) km/h, and 12 minutes is 1/5 hour, so the distance is

\[ 25 \times \frac{12}{60} = 5 \text{ km} \]

True. A common slip in statement 1 is to subtract the current only once (15 − 2.5 = 12.5) and stop there.

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7.

If the speed of a boat in still water is 20 kmph and the speed of the current is 5 kmph, then the time taken by the boat to travel 100 kms with the current is?

Exam Year(s)

ISRO Assistant - 2023,

Answer: C

The time taken is 4 hours.

With the current, the boat's speed is the still-water speed plus the current's speed:

\[ \begin{aligned} v &= 20 + 5 = 25\ \text{km/h} \\ t &= 100/25 = 4\ \text{h} \end{aligned} \]

Against the current the speed would be 15 km/h and the time about 6.7 hours. 2 and 3 hours would need speeds of 50 and 33 km/h, and 7 hours matches no speed in the question.

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8.

The speed of a swimmer in still water is 20 kmph and the rate of flow of the river is 4 kmph. Moving with the stream the swimmer went 120 km. What distance will the swimmer cover during the same time going against the stream?

Exam Year(s)

ISRO Assistant - 2023,

Answer: B

Against the stream the swimmer covers 80 km.

Downstream speed is 20 + 4 = 24 km/h and upstream speed is 20 - 4 = 16 km/h:

\[ \begin{aligned} t &= 120/24 = 5\ \text{h} \\ d &= 16 \times 5 = 80\ \text{km} \end{aligned} \]

Equivalently, in equal times distances are in the ratio of speeds, 120 \(\times\) 16/24 = 80. 90 and 75 km come from taking 18 or 15 km/h as the upstream speed.

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9.

A man rows 27 km with the stream and 15 km against the stream taking 4 hours each time. Find the rate at which the stream flows?

Exam Year(s)

ISRO Assistant - 2023,

Answer: A

The stream flows at 1.5 kmph.

Downstream speed is 27/4 = 6.75 km/h and upstream speed is 15/4 = 3.75 km/h. The stream's speed is half their difference:

\[ \frac{6.75 - 3.75}{2} = 1.5\ \text{km/h} \]

The rowing speed in still water is half the sum, 5.25 km/h. Taking the full difference (3 km/h) is the usual error; 1.8, 2.2 and 2.5 do not follow.

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10.

A group of men can row a canoe at 40 kilometers per hour in still water. After rowing for 2 hours the stream flows downhill and they take two more hours to reach a point. On the way back by the same route the time taken is two times the time taken for onward journey. What is the speed of the stream?

Exam Year(s)

Kerala PSC KAS - 2020,

Answer: B

The speed of the stream is 20 km/hour.

Onward: 2 hours in still water at 40 km/h covers 80 km, then 2 hours downstream at \(40 + s\) covers \(2(40 + s)\) km, a total of 4 hours. The return takes twice as long, 8 hours: the still stretch again takes 2 hours, so the upstream stretch takes 6 hours at \(40 - s\).

\[ \begin{aligned} \frac{2(40 + s)}{40 - s} &= 6 \\ 80 + 2s &= 240 - 6s \\ 8s &= 160 \\ s &= 20 \end{aligned} \]

Check: downstream at 60 km/h for 2 hours covers 120 km, and upstream at 20 km/h the same 120 km takes 6 hours. With 40 km/h the boat could not move upstream at all, which rules out that option.

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