# Boats and Streams Quiz Set 016

### 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

Two similar boats, A and B, start to move towards each other. If they meet when A has travelled \$(1/6)\$th of the distance, what is the ratio of the upstream speed to the downstream speed of a boat in that river?

A

5.

B

6.

C

4.

D

7.

Soln.
Ans: a

The boats are same, so they have the same speed in still water. Let the upstream speed be u and v be the downstream speed, and let the initial distance between them be L. When they meet they have travelled for the same time. So \$(L/6)/u = ({5L}/6)/v\$. The ratio \$v/u\$ = 5.

### Question 3

A boat can travel 128 km downstream in 16 hours. If it covers the same distance upstream in 32 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 = \$128/16\$ = 8 km/h, and the upstream speed = \$128/32\$ = 4 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 = \${8 + 4}/2\$ = 6 km/h.

### Question 4

A boat has a speed of 3 km/h in a still stream. What is the speed downstream in a stream that is flowing at a speed of 2 km/h?

A

5 kmph.

B

6 kmph.

C

4 kmph.

D

8 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 3 + 2 = 5 km/h.

### Question 5

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

A

8.

B

10.

C

12.

D

16.

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 = 8. 