# Boats and Streams Quiz Set 014

### Question 1

The speed of a boat in still water is 95 km/h. It takes the same time to travel an upstream distance of 7 km as it takes to travel a downstream distance of 12 km. The rate of flow of the stream is?

A

25 km/h.

B

26 km/h.

C

24 km/h.

D

28 km/h.

Soln.
Ans: a

Let v km/h be the rate of flow of the stream. Upstream and downstream times are equal. So \$7/{95 - v}\$ = \$12/{95 + v}\$. Solving for v, or verifying by putting the given options one by one, we get v = 25 km/h.

### Question 2

An airplane can travel at \$3{1/5}\$ km/h in still air. But it takes thrice as much time to travel upstream as compared to the time it takes downstream, if air is blowing at a rate of R km/h. What is R?

A

\$1{3/5}\$ km/h.

B

\$3{1/4}\$ km/h.

C

\${3/7}\$ km/h.

D

\$3{2/7}\$ km/h.

Soln.
Ans: a

If the distance travelled is D, we have \$D/{16/5 - R}\$ = 3 × \$D/{16/5 + R}\$. Cancelling D, and solving for R, we get R = \${8/5}\$, which is same as: \$1{3/5}\$ km/h.

### Question 3

A boat has a speed of 5 km/h in a still stream. What is the speed downstream in a stream that is flowing at a speed of 2 km/h?

A

7 kmph.

B

8 kmph.

C

6 kmph.

D

10 kmph.

Soln.
Ans: a

The downstream speed is the speed along the direction of the flow of the stream. It is equal to the sum of the speed of the boat in still water and the speed of the stream. So the speed downstream is 5 + 2 = 7 km/h.

### Question 4

If the speed of a boat in the direction of the stream current is 28 km/h, and the speed of the current is 12 km/h, what would be the speed of the boat against the current?

A

4 km/h.

B

5 km/h.

C

3 km/h.

D

7 km/h.

Soln.
Ans: a

Speed of the boat in still water is the difference between its downstream speed and the speed of the stream, which is 28 - 12 = 16 km/h. Hence, the speed of the boat against the current is 16 - 12 = 4 km/h.

### Question 5

A man can row at \$1{3/13}\$ km/h in still water and finds that it takes him thrice as much time to row up than as to row down the same distance in the river. The downstream speed of the man is?

A

\$1{11/13}\$ km/h.

B

\$3{1/12}\$ km/h.

C

\${11/15}\$ km/h.

D

\$4{1/5}\$ km/h.

Soln.
Ans: a

If the distance travelled is D and the speed of the current is R km/h, we have \$D/{16/13 - R}\$ = 3 × \$D/{16/13 + R}\$. Cancelling D, and solving for R, we get R = \${8/13}\$ km/h. So downstream speed would be \${8/13}\$ + \$16/13\$ = \$1{11/13}\$ km/h. 