# Boats and Streams Quiz Set 002

### Question 1

The speed of a boat in still water is 84 km/h. It takes the same time to travel an upstream distance of 9 km as it takes to travel a downstream distance of 19 km. The rate of flow of the stream is?

A

30 km/h.

B

31 km/h.

C

29 km/h.

D

33 km/h.

Soln.
Ans: a

Let v km/h be the rate of flow of the stream. Upstream and downstream times are equal. So \$9/{84 - v}\$ = \$19/{84 + v}\$. Solving for v, or verifying by putting the given options one by one, we get v = 30 km/h.

### Question 2

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 3

The speed of a boat in still water is 10 km/h and rate of flow of the stream is 4 km/h. If it travels upstream for 5 hours, what is the distance travelled by the boat during the journey?

A

30 km.

B

31 km.

C

29 km.

D

33 km.

Soln.
Ans: a

The effective speed of the boat in the stream is 10 - 4 = 6 km/h. The distance is speed × time = 6 × 5 = 30 km.

### Question 4

Two similar boats, A and B, start to move towards each other. If they meet when A has travelled \$(1/5)\$th of the distance, what is the ratio of the upstream speed to the downstream speed of a boat in that river?

A

4.

B

5.

C

3.

D

6.

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/5)/u = ({4L}/5)/v\$. The ratio \$v/u\$ = 4.

### Question 5

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{1/2}\$. What is the speed of the river?

A

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

B

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

C

\$3{1/2}\$ units.

D

\$2{1/4}\$ 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{1/2}\$.