# Boats and Streams Quiz Set 005

### Question 1

The speed of a steamer in still water, the upstream speed of the steamer and the downstream speed of the steamer form an A.P.(Arithmetic Progression) whose common difference is \$1{1/6}\$. What is the speed of the river?

A

\$1{1/6}\$ units.

B

\$2{3/5}\$ units.

C

\$2{3/8}\$ units.

D

\$3{1/8}\$ units.

Soln.
Ans: a

Let the speed of the steamer in still water be u and the speed of the river 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. Since v is also the speed of the river, the required answer is: \$1{1/6}\$.

### Question 2

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 3

A steamer boat can travel 200 km downstream in 20 hours. If it covers the same distance upstream in 50 hours, what is the speed of the boat in still water?

A

7 kmph.

B

8 kmph.

C

6 kmph.

D

10 kmph.

Soln.
Ans: a

The downstream speed = \$200/20\$ = 10 km/h, and the upstream speed = \$200/50\$ = 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 = \${10 + 4}/2\$ = 7 km/h.

### Question 4

The speed of a boat in still water is 16 km/h and rate of flow of the stream is 6 km/h. If it travels upstream for 7 hours, what is the distance travelled by the boat during the journey?

A

70 km.

B

71 km.

C

69 km.

D

73 km.

Soln.
Ans: a

The effective speed of the boat in the stream is 16 - 6 = 10 km/h. The distance is speed × time = 10 × 7 = 70 km.

### Question 5

A man can row a boat at the rate of 12 km/h in still water, and at the rate of 8 km/h against the stream. At what rate can he row down the stream?

A

16 km/h.

B

17 km/h.

C

15 km/h.

D

19 km/h.

Soln.
Ans: a

If v is the speed of the stream, 12 - v = 8, so the speed of the stream is 12 - 8 = 4 km/h. So his downstream speed would be 12 + 4 = 16 km/h. 