# Boats and Streams Quiz Set 006

### Question 1

A man can row at \$2{2/5}\$ km/h in still water and finds that it takes him thrice as much time to row up than as to row down the same distance in the river. The downstream speed of the man is?

A

\$3{3/5}\$ km/h.

B

\$5{3/4}\$ km/h.

C

\$1{6/7}\$ km/h.

D

\$4{5/7}\$ km/h.

Soln.
Ans: a

If the distance travelled is D and the speed of the current is R km/h, we have \$D/{12/5 - R}\$ = 3 × \$D/{12/5 + R}\$. Cancelling D, and solving for R, we get R = \${6/5}\$ km/h. So downstream speed would be \${6/5}\$ + \$12/5\$ = \$3{3/5}\$ km/h.

### Question 2

A boat can travel 300 km downstream in 30 hours. If it covers the same distance upstream in 50 hours, what is the speed of the boat in still water?

A

8 kmph.

B

9 kmph.

C

7 kmph.

D

11 kmph.

Soln.
Ans: a

The downstream speed = \$300/30\$ = 10 km/h, and the upstream speed = \$300/50\$ = 6 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 = \${10 + 6}/2\$ = 8 km/h.

### Question 3

Two similar boats, A and B, start to move towards each other. If they meet when A has travelled \$(1/6)\$th of the distance, what is the ratio of the upstream speed to the downstream speed of a boat in that river?

A

5.

B

6.

C

4.

D

7.

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/6)/u = ({5L}/6)/v\$. The ratio \$v/u\$ = 5.

### Question 4

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 \${4/9}\$. What is the speed of the river?

A

\${4/9}\$ units.

B

\$1{5/8}\$ units.

C

2 units.

D

\$2{9/11}\$ 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: \${4/9}\$.

### Question 5

The speed of a boat in still water is 112 km/h. It takes the same time to travel an upstream distance of 2 km as it takes to travel a downstream distance of 14 km. The rate of flow of the stream is?

A

84 km/h.

B

85 km/h.

C

83 km/h.

D

87 km/h.

Soln.
Ans: a

Let v km/h be the rate of flow of the stream. Upstream and downstream times are equal. So \$2/{112 - v}\$ = \$14/{112 + v}\$. Solving for v, or verifying by putting the given options one by one, we get v = 84 km/h. 