Competitive Exams : Quantitative Aptitude - Boats (Set 1) | Concept of Maths

Question 1

1. A boat goes 12 km downstream in 1 hour. If the speed of the stream is 2 km/h, what is the speed of the boat in still water?

A) 14 km/h

B) 10 km/h

C) 8 km/h

D) 12 km/h

Answer

Correct Answer: B

Solution: Downstream Speed ($D$) = 12 km/h. Stream Speed ($v$) = 2 km/h. Still water speed ($u$) = $D - v = 12 - 2 = 10$ km/h.

Question 2

2. If the speed of a boat in still water is 8 km/h and the speed of the stream is 3 km/h, what is the upstream speed?

A) 11 km/h

B) 8 km/h

C) 5 km/h

D) 13 km/h

Answer

Correct Answer: C

Solution: Upstream Speed ($U$) = Speed in still water ($u$) - Speed of stream ($v$). $U = 8 - 3 = 5$ km/h.

Question 3

3. The downstream speed of a boat is 15 km/h and the upstream speed is 9 km/h. Find the speed of the boat in still water.

A) 12 km/h

B) 6 km/h

C) 3 km/h

D) 24 km/h

Answer

Correct Answer: A

Solution: Still water speed ($u$) = $\frac{D + U}{2} = \frac{15 + 9}{2} = 12$ km/h.

Question 4

4. A boat covers 20 km upstream in 5 hours. What is the upstream speed?

A) 10 km/h

B) 15 km/h

C) 5 km/h

Question 5

5. If a man can row 5 km/h in still water and the rate of current is 1 km/h, how long will he take to row 24 km downstream?

A) 6 hours

B) 4 hours

C) 8 hours

D) 12 hours

Answer

Correct Answer: B

Solution: Downstream speed = $5 + 1 = 6$ km/h. Time = $\frac{\text{Distance}}{\text{Speed}} = \frac{24}{6} = 4$ hours.

Question 6

6. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?

A) 1 hour

B) 45 minutes

C) 1 hour 15 minutes

D) 2 hours

Answer

Correct Answer: C

Solution: Upstream ($U$) = 2 km/h. Downstream ($D$) = 1 km in 10 min = 6 km/h. Still water speed ($u$) = $\frac{6 + 2}{2} = 4$ km/h. Time for 5 km = $\frac{5}{4} = 1.25$ hours = 1 hr 15 min.

Question 7

7. Find the speed of the stream if the downstream speed is 18 km/h and the upstream speed is 10 km/h.

A) 4 km/h

B) 8 km/h

C) 14 km/h

D) 2 km/h

Answer

Correct Answer: A

Solution: Stream Speed ($v$) = $\frac{D - U}{2} = \frac{18 - 10}{2} = 4$ km/h.

Question 8

8. A man rows 750 m in 675 seconds against the stream and returns in $7\frac{1}{2}$ minutes. His speed in still water is:

A) 4 km/h

B) 6 km/h

C) 5 km/h

D) 3 km/h

Answer

Correct Answer: C

Solution: Upstream Speed = $\frac{750}{675} = \frac{10}{9}$ m/s. Downstream Speed = $\frac{750}{450} = \frac{5}{3}$ m/s. Speed in still water = $\frac{1}{2} \times (\frac{10}{9} + \frac{15}{9}) = \frac{25}{18}$ m/s. Convert to km/h: $\frac{25}{18} \times \frac{18}{5} = 5$ km/h.

Question 9

9. A boat travels 32 km downstream in 4 hours and 24 km upstream in 6 hours. What is the speed of the stream?

A) 1 km/h

B) 2 km/h

C) 4 km/h

D) 6 km/h

Answer

Correct Answer: B

Solution: $D = \frac{32}{4} = 8$ km/h. $U = \frac{24}{6} = 4$ km/h. Stream Speed ($v$) = $\frac{8 - 4}{2} = 2$ km/h.

Question 10

10. In one hour, a boat goes 11 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/h) is:

A) 3

B) 5

C) 9

D) 8

Answer

Correct Answer: D

Solution: $D = 11$ km/h, $U = 5$ km/h. Speed in still water = $\frac{11 + 5}{2} = 8$ km/h.

Accepted Answer

Correct Answer: D

Solution: Speed = $\frac{\text{Distance}}{\text{Time}}$. Upstream speed = $\frac{20}{5} = 4$ km/h.

Competitive Exams : Quantitative Aptitude - Boats (Set 1) | Concept of Maths