# Boats and Streams Quiz Set 017

### Question 1

A man can row at \$2{2/5}\$ 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

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

B

\$5{3/4}\$ km/h.

C

\$1{6/7}\$ km/h.

D

\$4{5/7}\$ km/h.

Soln.
Ans: a

If the distance travelled is D and the speed of the current is R km/h, we have \$D/{12/5 - R}\$ = 3 × \$D/{12/5 + R}\$. Cancelling D, and solving for R, we get R = \${6/5}\$ km/h. So downstream speed would be \${6/5}\$ + \$12/5\$ = \$3{3/5}\$ km/h.

### Question 2

A boat has a downstream speed of 14 km/h and an upstream speed of 8 km/h. What is the speed of the boat in still water?

A

11 kmph.

B

12 kmph.

C

10 kmph.

D

14 kmph.

Soln.
Ans: a

By the shortcut method, the speed of the boat in still water is average of downstream and upstream speeds. So the required speed = \${14 + 8}/2\$ = 11 km/h.

### Question 3

A steamer boat can travel 280 km downstream in 20 hours. If it covers the same distance upstream in 70 hours, what is the speed of the boat in still water?

A

9 kmph.

B

10 kmph.

C

8 kmph.

D

12 kmph.

Soln.
Ans: a

The downstream speed = \$280/20\$ = 14 km/h, and the upstream speed = \$280/70\$ = 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 = \${14 + 4}/2\$ = 9 km/h.

### Question 4

A boat has a downstream speed of 14 km/h and an upstream speed of 4 km/h. What is the speed of the stream?

A

5 kmph.

B

6 kmph.

C

4 kmph.

D

8 kmph.

Soln.
Ans: a

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 - 4}/2\$ = 5 km/h.

### Question 5

The upstream journey of a boat takes 8 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

\$1{2/7}\$.

B

\$2{2/3}\$.

C

\${2/9}\$.

D

\$3{1/3}\$.

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} = 8 × L/{u + v}\$. We can solve this equation for u/v to get u/v = \${8 + 1}/{8 - 1}\$ = \$1{2/7}\$. 