# Boats and Streams Quiz Set 010

### Question 1

A boat can travel 392 km downstream in 28 hours. If it covers the same distance upstream in 98 hours, what is the rate of flow of the stream?

A

5 kmph.

B

6 kmph.

C

4 kmph.

D

8 kmph.

Soln.
Ans: a

The downstream speed = \$392/28\$ = 14 km/h, and the upstream speed = \$392/98\$ = 4 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 - 4}/2\$ = 5 km/h.

### Question 2

A boat has a downstream speed of 8 km/h and an upstream speed of 6 km/h. 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

By the shortcut method, the speed of the boat in still water is average of downstream and upstream speeds. So the required speed = \${8 + 6}/2\$ = 7 km/h.

### Question 3

The speed of a boat in still water is 12 km/h and rate of flow of the stream is 4 km/h. If it travels upstream for 6 hours, what is the distance travelled by the boat during the journey?

A

48 km.

B

49 km.

C

47 km.

D

51 km.

Soln.
Ans: a

The effective speed of the boat in the stream is 12 - 4 = 8 km/h. The distance is speed × time = 8 × 6 = 48 km.

### Question 4

The speed of an aircraft in still air is 14 km/h and rate of wind is 4 km/h. If it travels along the direction of the wind for 3 hours, what is the distance travelled by the aircraft during the journey?

A

54 km.

B

55 km.

C

53 km.

D

57 km.

Soln.
Ans: a

The effective speed of the aircraft in the air is 14 + 4 = 18 km/h. The distance is speed × time = 18 × 3 = 54 km.

### Question 5

The product of the downstream and upstream speeds of a boat in a river is 8. What is the difference between the squares of the speed of the boat in still water and the speed of the stream?

A

8.

B

10.

C

12.

D

16.

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 = 8. 