Boats and Streams Quiz Set 020

Question 1

Two similar boats, A and B, start to move towards each other. If they meet when A has travelled \$(1/8)\$th of the distance, what is the ratio of the upstream speed to the downstream speed of a boat in that river?

A

7.

B

8.

C

6.

D

9.

Soln.
Ans: a

The boats are same, so they have the same speed in still water. Let the upstream speed be u and v be the downstream speed, and let the initial distance between them be L. When they meet they have travelled for the same time. So \$(L/8)/u = ({7L}/8)/v\$. The ratio \$v/u\$ = 7.

Question 2

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 3

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.

Question 4

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. What is the speed of the boat in still water?

A

1 units.

B

2 units.

C

3 units.

D

\$1{1/3}\$ 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.

Question 5

A boat can travel 512 km downstream in 32 hours. If it covers the same distance upstream in 64 hours, what is the rate of flow of the stream?

A

4 kmph.

B

5 kmph.

C

3 kmph.

D

7 kmph.

Soln.
Ans: a

The downstream speed = \$512/32\$ = 16 km/h, and the upstream speed = \$512/64\$ = 8 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 = \${16 - 8}/2\$ = 4 km/h. 