# Boats and Streams Quiz Set 018

### Question 1

A boat travels a downstream distance of 70 km in 7 hours, and an upstream distance of 24 km in 6 hours. What is the speed of the stream?

A

3 kmph.

B

4 kmph.

C

2 kmph.

D

6 kmph.

Soln.
Ans: a

The downstream speed = \$70/7\$ = 10 km/h, and the upstream speed = \$24/6\$ = 4 km/h. By the shortcut method, the speed of the stream is half of the difference between the downstream and upstream speeds of the boat. So the required speed = \${10 - 4}/2\$ = 3 km/h.

### Question 2

A man can row at \$1{5/7}\$ 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

\$2{4/7}\$ km/h.

B

\$4{1/6}\$ km/h.

C

\$1{2/9}\$ km/h.

D

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

Soln.
Ans: a

If the distance travelled is D and the speed of the current is R km/h, we have \$D/{12/7 - R}\$ = 3 × \$D/{12/7 + R}\$. Cancelling D, and solving for R, we get R = \${6/7}\$ km/h. So downstream speed would be \${6/7}\$ + \$12/7\$ = \$2{4/7}\$ km/h.

### Question 3

A boat has a speed of 7 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

9 kmph.

B

10 kmph.

C

8 kmph.

D

12 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 7 + 2 = 9 km/h.

### Question 4

The product of the downstream and upstream speeds of a boat in a river is 12. What is the difference between the squares of the speed of the boat in still water and the speed of the stream?

A

12.

B

14.

C

16.

D

20.

Soln.
Ans: a

Let the speed of the boat in still water be u, and let v be the speed of the stream. The product of the upstream and downstream speeds of the boat is \$(u + v) × (u - v)\$, which is \$u^2 - v^2\$, and, therefore, the required answer = 12.

### Question 5

A boat travels a downstream distance of 28 km in 2 hours, and an upstream distance of 56 km in 4 hours. What is the speed of the stream?

A

0 kmph.

B

1 kmph.

C

2 kmph.

D

3 kmph.

Soln.
Ans: a

The downstream speed = \$28/2\$ = 14 km/h, and the upstream speed = \$56/4\$ = 14 km/h. By the shortcut method, the speed of the stream is half of the difference between the downstream and upstream speeds of the boat. So the required speed = \${14 - 14}/2\$ = 0 km/h. 