# Boats and Streams Quiz Set 001

### Question 1

A boat has a downstream speed of 12 km/h and an upstream speed of 12 km/h. What is the speed of the boat in still water?

A

12 kmph.

B

13 kmph.

C

11 kmph.

D

15 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 = \${12 + 12}/2\$ = 12 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

The difference of the squares of the downstream and upstream speeds of a boat in a stream is 12. What is the product of the speed of the stream and that of the boat in still water?

A

3.

B

4.

C

2.

D

6.

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 = 12. We get uv = \$12/4\$ = 3.

### 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

A man can row a boat at the rate of 12 km/h in still water, and at the rate of 6 km/h against the stream. At what rate can he row down the stream?

A

18 km/h.

B

19 km/h.

C

17 km/h.

D

21 km/h.

Soln.
Ans: a

If v is the speed of the stream, 12 - v = 6, so the speed of the stream is 12 - 6 = 6 km/h. So his downstream speed would be 12 + 6 = 18 km/h.