# Boats and Streams Quiz Set 007

### Question 1

The speed of a boat in still water is 28 km/h. It takes the same time to travel an upstream distance of 2 km as it takes to travel a downstream distance of 12 km. The rate of flow of the stream is?

A

20 km/h.

B

21 km/h.

C

19 km/h.

D

23 km/h.

Soln.
Ans: a

Let v km/h be the rate of flow of the stream. Upstream and downstream times are equal. So \$2/{28 - v}\$ = \$12/{28 + v}\$. Solving for v, or verifying by putting the given options one by one, we get v = 20 km/h.

### Question 2

A boat can travel 1152 km downstream in 72 hours. If it covers the same distance upstream in 96 hours, what is the speed of the boat in still water?

A

14 kmph.

B

15 kmph.

C

13 kmph.

D

17 kmph.

Soln.
Ans: a

The downstream speed = \$1152/72\$ = 16 km/h, and the upstream speed = \$1152/96\$ = 12 km/h. By the shortcut method, the speed of the boat in still water is average of the downstream and upstream speeds of the boat. So the required speed = \${16 + 12}/2\$ = 14 km/h.

### Question 3

A man can row a boat at the rate of 12 km/h in still water, and at the rate of 6 km/h against the stream. At what rate can he row down the stream?

A

18 km/h.

B

19 km/h.

C

17 km/h.

D

21 km/h.

Soln.
Ans: a

If v is the speed of the stream, 12 - v = 6, so the speed of the stream is 12 - 6 = 6 km/h. So his downstream speed would be 12 + 6 = 18 km/h.

### Question 4

The speed of a steamer in still water, the upstream speed of the steamer and the downstream speed of the steamer form an A.P.(Arithmetic Progression) whose common difference is 1. What is the speed of the river?

A

1 units.

B

2 units.

C

3 units.

D

\$1{1/3}\$ units.

Soln.
Ans: a

Let the speed of the steamer in still water be u and the speed of the river be v. The three speeds are u - v, u and u + v. They are in an A.P. with a common difference equal to v. Since v is also the speed of the river, the required answer is: 1.

### Question 5

A steamer boat can travel 64 km downstream in 8 hours. If it covers the same distance upstream in 16 hours, what is the speed of the boat in still water?

A

6 kmph.

B

7 kmph.

C

5 kmph.

D

9 kmph.

Soln.
Ans: a

The downstream speed = \$64/8\$ = 8 km/h, and the upstream speed = \$64/16\$ = 4 km/h. By the shortcut method, the speed of the steamer boat in still water is average of its downstream and upstream speeds. So the required speed = \${8 + 4}/2\$ = 6 km/h. 