# Boats and Streams Quiz Set 012

### Question 1

A boat has a downstream speed of 16 km/h and an upstream speed of 6 km/h. What is the speed of the stream?

A

5 kmph.

B

6 kmph.

C

4 kmph.

D

8 kmph.

Soln.
Ans: a

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 = \${16 - 6}/2\$ = 5 km/h.

### Question 2

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. What is the speed of the river?

A

1 units.

B

2 units.

C

3 units.

D

\$1{1/3}\$ 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.

### Question 3

A boat has a downstream speed of 14 km/h and an upstream speed of 4 km/h. What is the speed of the stream?

A

5 kmph.

B

6 kmph.

C

4 kmph.

D

8 kmph.

Soln.
Ans: a

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 - 4}/2\$ = 5 km/h.

### Question 4

A boat can travel 192 km downstream in 16 hours. If it covers the same distance upstream in 24 hours, what is the speed of the boat in still water?

A

10 kmph.

B

11 kmph.

C

9 kmph.

D

13 kmph.

Soln.
Ans: a

The downstream speed = \$192/16\$ = 12 km/h, and the upstream speed = \$192/24\$ = 8 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 + 8}/2\$ = 10 km/h.

### Question 5

The speed of an aircraft in still air is 10 km/h and rate of wind is 4 km/h. If it travels along the direction of the wind for 4 hours, what is the distance travelled by the aircraft during the journey?

A

56 km.

B

57 km.

C

55 km.

D

59 km.

Soln.
Ans: a

The effective speed of the aircraft in the air is 10 + 4 = 14 km/h. The distance is speed × time = 14 × 4 = 56 km. 