Boats and Streams Quiz Set 001

Question 1

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{1/5}\$. What is the speed of the boat in still water?

A

\$1{1/5}\$ units.

B

\$2{3/4}\$ units.

C

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

D

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: \$1{1/5}\$.

Question 2

A boat can travel 288 km downstream in 24 hours. If it covers the same distance upstream in 72 hours, what is the speed of the boat in still water?

A

8 kmph.

B

9 kmph.

C

7 kmph.

D

11 kmph.

Soln.
Ans: a

The downstream speed = \$288/24\$ = 12 km/h, and the upstream speed = \$288/72\$ = 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 = \${12 + 4}/2\$ = 8 km/h.

Question 3

The speed of an aircraft in still air is 12 km/h and rate of wind is 8 km/h. If it travels along the direction of the wind for 8 hours, what is the distance travelled by the aircraft during the journey?

A

160 km.

B

161 km.

C

159 km.

D

163 km.

Soln.
Ans: a

The effective speed of the aircraft in the air is 12 + 8 = 20 km/h. The distance is speed × time = 20 × 8 = 160 km.

Question 4

The difference of the squares of the downstream and upstream speeds of a boat in a stream is 28. What is the product of the speed of the stream and that of the boat in still water?

A

7.

B

8.

C

6.

D

10.

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 = 28. We get uv = \$28/4\$ = 7.

Question 5

The upstream journey of a boat takes 8 times the time it takes it to complete the downstream journey. What is the ratio of the speed of the boat in still water to the speed of the stream?

A

\$1{2/7}\$.

B

\$2{2/3}\$.

C

\${2/9}\$.

D

\$3{1/3}\$.

Soln.
Ans: a

Let the distance be L and the speed of the boat in still water be u, with v being the speed of the stream. We are given \$L/{u - v} = 8 × L/{u + v}\$. We can solve this equation for u/v to get u/v = \${8 + 1}/{8 - 1}\$ = \$1{2/7}\$. This Blog Post/Article "Boats and Streams Quiz Set 001" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2019-08-18.