# Boats and Streams Quiz Set 013

### Question 1

An airplane can travel at 2 km/h in still air. But it takes thrice as much time to travel upstream as compared to the time it takes downstream, if air is blowing at a rate of R km/h. What is R?

A

1 km/h.

B

2 km/h.

C

3 km/h.

D

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

Soln.
Ans: a

If the distance travelled is D, we have \$D/{2/1 - R}\$ = 3 × \$D/{2/1 + R}\$. Cancelling D, and solving for R, we get R = 1 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 2. What is the speed of the boat in still water?

A

2 units.

B

3 units.

C

4 units.

D

\$1{2/3}\$ 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: 2.

### Question 3

A boat has a downstream speed of 12 km/h and an upstream speed of 8 km/h. What is the speed of the stream?

A

2 kmph.

B

3 kmph.

C

4 kmph.

D

5 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 = \${12 - 8}/2\$ = 2 km/h.

### Question 4

The difference of the squares of the downstream and upstream speeds of a boat in a stream is 8. What is the product of the speed of the stream and that of the boat in still water?

A

2.

B

3.

C

4.

D

5.

Soln.
Ans: a

Let the speed of the boat in still water be u, and let v be the speed of the stream. The difference of squares of the speeds is \$(u + v)^2 - (u - v)^2\$, which is \$u^2 + v^2 + 2uv - (u^2 + v^2 - 2uv)\$ = 4uv = 8. We get uv = \$8/4\$ = 2.

### Question 5

A steamer boat can travel 560 km downstream in 40 hours. If it covers the same distance upstream in 70 hours, 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

The downstream speed = \$560/40\$ = 14 km/h, and the upstream speed = \$560/70\$ = 8 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 + 8}/2\$ = 11 km/h. 