# Boats and Streams Quiz Set 011

### Question 1

If the speed of a boat in the direction of the stream current is 18 km/h, and the speed of the current is 4 km/h, what would be the speed of the boat against the current?

A

10 km/h.

B

11 km/h.

C

9 km/h.

D

13 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 18 - 4 = 14 km/h. Hence, the speed of the boat against the current is 14 - 4 = 10 km/h.

### Question 2

The speed of a boat in still water, the upstream speed of the boat and the downstream speed of the boat form an A.P.(Arithmetic Progression) whose middle term is \$1{1/8}\$. What is the speed of the boat in still water?

A

\$1{1/8}\$ units.

B

\$2{3/7}\$ units.

C

\$2{1/2}\$ units.

D

\$3{3/10}\$ units.

Soln.
Ans: a

Let the speed of the boat in still water be u and the speed of the stream 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, and u as its middle term. Since u is also the speed of the boat in still water, the required answer is: \$1{1/8}\$.

### Question 3

A boat has a downstream speed of 6 km/h and an upstream speed of 4 km/h. What is the speed of the boat in still water?

A

5 kmph.

B

6 kmph.

C

4 kmph.

D

8 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 = \${6 + 4}/2\$ = 5 km/h.

### Question 4

A boat has a speed of 4 km/h in a still stream. What is the speed downstream in a stream that is flowing at a speed of 3 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 4 + 3 = 7 km/h.

### Question 5

If the speed of a boat in the direction of the stream current is 24 km/h, and the speed of the current is 8 km/h, what would be the speed of the boat against the current?

A

8 km/h.

B

9 km/h.

C

7 km/h.

D

11 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 24 - 8 = 16 km/h. Hence, the speed of the boat against the current is 16 - 8 = 8 km/h. 