# Boats and Streams Quiz Set 003

### Question 1

The upstream journey of a boat takes 3 times the time it takes it to complete the downstream journey. What is the ratio of the speed of the boat in still water to the speed of the stream?

A

2.

B

3.

C

4.

D

\$1{2/3}\$.

Soln.
Ans: a

Let the distance be L and the speed of the boat in still water be u, with v being the speed of the stream. We are given \$L/{u - v} = 3 × L/{u + v}\$. We can solve this equation for u/v to get u/v = \${3 + 1}/{3 - 1}\$ = 2.

### Question 2

A steamer boat can travel 480 km downstream in 30 hours. If it covers the same distance upstream in 48 hours, what is the speed of the boat in still water?

A

13 kmph.

B

14 kmph.

C

12 kmph.

D

16 kmph.

Soln.
Ans: a

The downstream speed = \$480/30\$ = 16 km/h, and the upstream speed = \$480/48\$ = 10 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 = \${16 + 10}/2\$ = 13 km/h.

### Question 3

A boat can travel 672 km downstream in 48 hours. If it covers the same distance upstream in 112 hours, what is the rate of flow of the stream?

A

4 kmph.

B

5 kmph.

C

3 kmph.

D

7 kmph.

Soln.
Ans: a

The downstream speed = \$672/48\$ = 14 km/h, and the upstream speed = \$672/112\$ = 6 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 - 6}/2\$ = 4 km/h.

### Question 4

The product of the downstream and upstream speeds of a boat in a river is 28. What is the difference between the squares of the speed of the boat in still water and the speed of the stream?

A

28.

B

30.

C

32.

D

36.

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 = 28.

### Question 5

A man can row at \$1{5/11}\$ 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{2/11}\$ km/h.

B

\$3{1/2}\$ km/h.

C

1 km/h.

D

\$4{5/13}\$ km/h.

Soln.
Ans: a

If the distance travelled is D and the speed of the current is R km/h, we have \$D/{16/11 - R}\$ = 3 × \$D/{16/11 + R}\$. Cancelling D, and solving for R, we get R = \${8/11}\$ km/h. So downstream speed would be \${8/11}\$ + \$16/11\$ = \$2{2/11}\$ km/h.