Competitive Exams : Quantitative Aptitude - Boats (Set 2) | Concept of Maths

Question 1

1. The ratio of the speed of a boat in still water to the speed of the stream is 8 : 1. If the boat travels 36 km downstream in 2 hours, find the speed of the stream.

A) 1 km/h

B) 2 km/h

C) 3 km/h

D) 4 km/h

Answer

Correct Answer: B

Solution: Downstream speed $D = \frac{36}{2} = 18$ km/h. Let speed of boat be $8x$ and stream be $x$. $D = 8x + x = 9x$. $9x = 18 \implies x = 2$. Speed of stream = 2 km/h.

Question 2

2. A boat covers 24 km upstream and 28 km downstream in 6 hours. It covers 30 km upstream and 21 km downstream in 6.5 hours. The speed of the stream is:

A) 2 km/h

B) 3 km/h

C) 4 km/h

D) 5 km/h

Answer

Correct Answer: C

Solution: Let $u$ be upstream and $d$ be downstream speed. $\frac{24}{u} + \frac{28}{d} = 6$ and $\frac{30}{u} + \frac{21}{d} = 6.5$. Solving these equations, we get $u = 6$ and $d = 14$. Speed of stream $v = \frac{d - u}{2} = \frac{14 - 6}{2} = 4$ km/h.

Question 3

3. A man can row 6 km/h in still water. If the speed of the current is 2 km/h, it takes him 3 hours more to go upstream than downstream for the same distance. The distance is:

A) 24 km

B) 30 km

C) 18 km

D) 32 km

Answer

Correct Answer: A

Solution: Boat speed $B = 6$, Current $C = 2$. Downstream $D = 8$, Upstream $U = 4$. Let distance be $x$. $\frac{x}{4} - \frac{x}{8} = 3$. $\frac{2x - x}{8} = 3 \implies \frac{x}{8} = 3 \implies x = 24$ km.

Question 4

4. 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 him to go 5 km in stationary water?

A) 40 minutes

B) 1 hour

C) 1 hour 30 mins

D) 1 hour 15 mins

Answer

Correct Answer: D

Solution: Upstream speed $U = 2$ km/h. Downstream speed $D = \frac{1}{10/60} = 6$ km/h. Speed in still water $B = \frac{6+2}{2} = 4$ km/h. Time to cover 5 km = $\frac{5}{4}$ = 1.25 hours = 1 hour 15 minutes.

Question 5

5. The speed of a boat in still water is 15 km/h and the speed of the current is 3 km/h. The distance travelled downstream in 12 minutes is:

A) 2.4 km

B) 1.8 km

C) 3.6 km

D) 4.2 km

Answer

Correct Answer: C

Solution: Downstream speed $D = 15 + 3 = 18$ km/h. Time = 12 mins = $\frac{12}{60}$ = 0.2 hours. Distance = $18 \times 0.2 = 3.6$ km.

Question 6

6. A boat takes half the time to move a certain distance downstream than upstream. What is the ratio between the speed of the boat in still water and the speed of the current?

A) 2 : 1

B) 3 : 1

C) 4 : 3

D) 5 : 2

Answer

Correct Answer: B

Solution: Let $D$ be downstream speed and $U$ be upstream speed. Time downstream = $\frac{1}{2}$ Time upstream $\implies D = 2U$. $B + C = 2(B - C) \implies B + C = 2B - 2C$. $B = 3C \implies B:C = 3:1$.

Question 7

7. A man rows to a place 48 km distant and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:

A) 1 km/h

B) 1.5 km/h

C) 2 km/h

D) 2.5 km/h

Answer

Correct Answer: A

Solution: Ratio of Downstream speed to Upstream speed = 4 : 3. Let $D = 4x$ and $U = 3x$. $\frac{48}{4x} + \frac{48}{3x} = 14 \implies \frac{12}{x} + \frac{16}{x} = 14$. $\frac{28}{x} = 14 \implies x = 2$. $D = 8, U = 6$. Speed of stream = $\frac{8 - 6}{2} = 1$ km/h.

Question 8

8. A boat moves downstream at the rate of 1 km in 7.5 minutes and upstream at the rate of 5 km an hour. What is the speed of the boat in still water?

A) 6 km/h

B) 5.5 km/h

C) 6.5 km/h

D) 7 km/h

Answer

Correct Answer: C

Solution: Downstream speed $D = \frac{1}{7.5/60} = \frac{60}{7.5} = 8$ km/h. Upstream speed $U = 5$ km/h. Speed in still water $B = \frac{D + U}{2} = \frac{8+5}{2} = 6.5$ km/h.

Question 9

9. Speed of a boat in standing water is 9 km/h and the speed of the stream is 1.5 km/h. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:

A) 20 hours

B) 24 hours

C) 28 hours

D) 18 hours

Answer

Correct Answer: B

Solution: $D = 9 + 1.5 = 10.5$ km/h; $U = 9 - 1.5 = 7.5$ km/h. Total time = $\frac{105}{10.5} + \frac{105}{7.5}$ = 10 + 14 = 24 hours.

Question 10

10. The speed of a boat in still water is 10 km/h. If it can travel 26 km downstream and 14 km upstream in the same time, the speed of the stream is:

A) 2 km/h

B) 4 km/h

C) 2.5 km/h

D) 3 km/h

Answer

Correct Answer: D

Solution: Let speed of stream be $x$. Time downstream = Time upstream. $\frac{26}{10 + x} = \frac{14}{10 - x} \implies 26(10 - x) = 14(10 + x)$. $260 - 26x = 140 + 14x \implies 40x = 120 \implies x = 3$ km/h.

Competitive Exams : Quantitative Aptitude - Boats (Set 2) | Concept of Maths