# Boats and Streams Quiz Set 019

### Question 1

A boat travels a downstream distance of 84 km in 6 hours, and an upstream distance of 40 km in 4 hours. What is the speed of the stream?

A

2 kmph.

B

3 kmph.

C

4 kmph.

D

5 kmph.

Soln.
Ans: a

The downstream speed = \$84/6\$ = 14 km/h, and the upstream speed = \$40/4\$ = 10 km/h. 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 = \${14 - 10}/2\$ = 2 km/h.

### Question 2

The product of the downstream and upstream speeds of a boat in a river is 20. What is the difference between the squares of the speed of the boat in still water and the speed of the stream?

A

20.

B

22.

C

24.

D

28.

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 = 20.

### Question 3

If the speed of a boat in the direction of the stream current is 16 km/h, and the speed of the current is 4 km/h, what would be the speed of the boat against the current?

A

8 km/h.

B

9 km/h.

C

7 km/h.

D

11 km/h.

Soln.
Ans: a

Speed of the boat in still water is the difference between its downstream speed and the speed of the stream, which is 16 - 4 = 12 km/h. Hence, the speed of the boat against the current is 12 - 4 = 8 km/h.

### Question 4

The upstream journey of a boat takes 6 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{2/5}\$.

B

3.

C

\${2/7}\$.

D

\$3{1/7}\$.

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} = 6 × L/{u + v}\$. We can solve this equation for u/v to get u/v = \${6 + 1}/{6 - 1}\$ = \$1{2/5}\$.

### Question 5

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 \${5/8}\$. What is the speed of the boat in still water?

A

\${5/8}\$ units.

B

\$1{6/7}\$ units.

C

\$2{1/10}\$ units.

D

\$2{9/10}\$ 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: \${5/8}\$. 