Logical Reasoning Questions for CLAT | QB Set 105 [Boats and Streams]

A river transport authority is conducting a training exercise to test the efficiency of two motorboats, Boat A and Boat B, on the same river. The river current flows at a constant speed of 3 km/h throughout the exercise. Boat A can travel at 18 km/h downstream and 12 km/h upstream. Boat B, which has a slightly less powerful engine, travels at 16 km/h downstream and 10 km/h upstream.

During the exercise, both boats are required to complete different journeys between checkpoints located along the river. The organisers calculate travel time using the effective speed of each boat depending on whether it is moving with or against the current. They also compare the boats on the basis of their speed in still water, total journey time and difference in arrival times.

For all calculations, assume that the boats maintain constant speeds, the river current does not change, and no time is lost while turning at a checkpoint. Distances between checkpoints are measured along the river, and all answers should be based only on the information given above.

Questions

1. What is the speed of Boat A in still water?

A. 15 km/h
B. 12 km/h
C. 18 km/h
D. 21 km/h

2. How much time will Boat B take to travel 40 km downstream?

A. 2 hours
B. 2.5 hours
C. 3 hours
D. 4 hours

3. Boat A travels 36 km downstream and then returns 36 km upstream. What is the total time taken for the entire journey?

A. 4 hours
B. 4.5 hours
C. 6 hours
D. 5 hours

4. Boat B travels 30 km upstream and then 32 km downstream. What is the total time taken?

A. 4 hours
B. 4.5 hours
C. 5 hours
D. 5.5 hours

5. Boat A and Boat B start together and travel 80 km downstream. Approximately how much earlier will Boat A reach the destination?

A. 20 minutes
B. 33 minutes 20 seconds
C. 40 minutes
D. 45 minutes

Answers and Detailed Explanations

1. Answer: A — 15 km/h

The relationship between downstream speed, speed in still water and speed of the current is:

Downstream Speed = Speed in Still Water + Current Speed

For Boat A:

18 = Speed in still water + 3

Therefore:

Speed in still water = 18 − 3 = 15 km/h

The same result can also be obtained using its upstream speed:

12 + 3 = 15 km/h

Hence, Option A is correct.

2. Answer: B — 2.5 hours

Boat B’s downstream speed is already given as 16 km/h.

Using:

Time = Distance ÷ Speed

Time = 40 ÷ 16

= 2.5 hours

Therefore, Boat B will take 2 hours and 30 minutes to cover 40 km downstream.

Hence, Option B is correct.

3. Answer: D — 5 hours

Boat A travels 36 km downstream and 36 km upstream.

Downstream Journey

Speed = 18 km/h

Time = 36 ÷ 18
= 2 hours

Upstream Journey

Speed = 12 km/h

Time = 36 ÷ 12
= 3 hours

Therefore:

Total time = 2 + 3
= 5 hours

Hence, Option D is correct.

4. Answer: C — 5 hours

Boat B travels 30 km upstream first.

Its upstream speed is 10 km/h.

Time taken upstream:

30 ÷ 10 = 3 hours

It then travels 32 km downstream at 16 km/h.

Time taken downstream:

32 ÷ 16 = 2 hours

Therefore:

Total time = 3 + 2
= 5 hours

Hence, Option C is correct.

5. Answer: B — 33 minutes 20 seconds

Both boats travel 80 km downstream.

Boat A

Downstream speed = 18 km/h

Time = 80 ÷ 18
= 40/9 hours
≈ 4.44 hours

Boat B

Downstream speed = 16 km/h

Time = 80 ÷ 16
= 5 hours

Difference:

5 − 40/9

= 45/9 − 40/9

= 5/9 hour

Converting this into minutes:

5/9 × 60
= 33⅓ minutes

⅓ minute = 20 seconds.

Therefore, the difference is approximately 33 minutes 20 seconds.

Hence, Option B is correct.