Problems on Boats and Streams(Set 4) - Solved Examples

Problems on Boats and Streams(Set 4) - Solved Examples

31. If a man's rate with the current is 15 km/hr and the rate of the current is 11⁄2 km/hr, then his rate against the current is
A. 12 km/hr	B. 10 km/hr
C. 10.5 km/hr	D. 12.5 km/hr

answer with explanation

Answer: Option A
Explanation:
Speed downstream = 15 km/hr
Rate of the current= 1¹⁄₂ km/hr

Speed in still water = 15 - 1¹⁄₂ = 13¹⁄₂ km/hr

Rate against the current = 13¹⁄₂ km/hr - 1¹⁄₂ = 12 km/hr

32. The speed of the boat in still water in 12 kmph. It can travel downstream through 45 kms in 3 hrs. In what time would it cover the same distance upstream?
A. 8 hours	B. 6 hours
C. 4 hours	D. 5 hours

answer with explanation

Answer: Option D
Explanation:
Speed of the boat in still water = 12 km/hr

Speed downstream $=\frac{45}{3}$ = 15 km/hr

Speed of the stream = 15-12 = 3 km/hr

Speed upstream = 12-3 = 9 km/hr

Time taken to cover 45 km upstream $=\frac{45}{9}$ = 5 hours

33. A boat goes 8 km upstream in 24 minutes. The speed of stream is 4 km/hr. The speed of boat in still water is:
A. 25 km/hr	B. 26 km/hr
C. 22 km/hr	D. 24 km/hr

answer with explanation

Answer: Option D
Explanation:
Speed upstream $=\frac{8}{\left(\frac{24}{60}\right)}$ = 20 km/hr

Speed of the stream = 4 km/hr

speed of boat in still water = (20+4) = 24 km/hr

34. The speed of a boat in still water is 25 kmph. If it can travel 10 km upstream in 1 hr, what time it would take to travel the same distance downstream?
A. 22 minutes	B. 30 minutes
C. 40 minutes	D. 15 minutes

answer with explanation

Answer: Option D
Explanation:
Speed of boat in still water = 25 km/hr

Speed upstream $=\frac{10}{1}$ = 10 km/hr

Speed of the stream = (25-10) = 15 km/hr

Speed downstream = (25+15) = 40 km/hr

Time taken to travel 10 km downstream $=\frac{10}{40}\text{hours}=\frac{10\times 60}{40}$ = 15 minutes

35. A boat can travel with a speed of 12 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.
A. 4 hr	B. 4.25 hr
C. 4.5 hr	D. 6 hr

answer with explanation

Answer: Option B
Explanation:
speed of boat in still water = 12 km/hr

speed of the stream = 4 km/hr

Speed downstream = (12+4) = 16 km/hr

Time taken to travel 68 km downstream $=\frac{68}{16}=\frac{17}{4}$ = 4.25 hours

36. A man can row 7.5 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.
A. 10 km/hr	B. 2.5 km/hr
C. 5 km/hr	D. 7.5 km/hr

answer with explanation

Answer: Option B
Explanation:
Given that, time taken to travel upstream = 2 × time taken to travel downstream

When distance is constant, speed is inversely proportional to the time
Hence, 2 × speed upstream = speed downstream

Let speed upstream $=x$
Then speed downstream $=2x$

we have, $\frac{1}{2}(x+2x)$ = speed in still water
$\Rightarrow \frac{1}{2}\left(3x\right)=7.5\Rightarrow 3x=15\Rightarrow x=5$

i.e., speed upstream = 5 km/hr

Rate of stream $=\frac{1}{2}(2x-x)=\frac{x}{2}=\frac{5}{2}=2.5\text{km/hr}$

37. A boat moves downstream at the rate of one km in 5 minutes and upstream at the rate of 4 km an hour. What is the velocity of the current?
A. 4 km/hr	B. 2 km/hr
C. 3 km/hr	D. 1 km/hr

answer with explanation

Answer: Option A
Explanation:
Speed downstream = $\frac{1}{\left(\frac{5}{60}\right)}=12\text{km/hr}$

Speed upstream $=\frac{4}{1}\text{= 4 km/hr}$

velocity of the current $=\frac{1}{2}(12-4)=\text{4 km/hr}$

38. The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 24 minutes is
A. 3.6 km	B. 2.4 km
C. 3.2 km	D. 7.2 km

answer with explanation

Answer: Option D
Explanation:
speed of a boat in still water = 15 km/hr
Speed of the current = 3 km/hr

Speed downstream = (15+3) = 18 km/hr

Distance travelled downstream in 24 minutes $=\frac{24}{60}\times 18=\frac{2\times 18}{5}\text{= 7.2 km}$

39. The current of a stream runs at the rate of 2 km per hr. A motor boat goes 10 km upstream and back again to the starting point in 55 min. Find the speed of the motor boat in still water?
A. 22 km/hr	B. 12 km/hr
C. 20 km/hr	D. 16 km/hr

answer with explanation

Answer: Option A
Explanation:
Let the speed of the boat in still water $=x$ km/hr
Speed of the current = 2 km/hr

Then, speed downstream $=(x+2)$ km/hr
speed upstream $=(x-2)$ km/hr

Total time taken to travel 10 km upstream and back = 55 minutes $=\frac{55}{60}$ hour = $\frac{11}{12}$hour
$\Rightarrow \frac{10}{x-2}+\frac{10}{x+2}=\frac{11}{12}120(x+2)+120(x-2)=11(x^2-4)240x=11x^2-4411x^2-240x-44=011x^2-242x+2x-44=011x(x-22)+2(x-22)=0(x-22)(11x+2)=0x=22\text{or}\frac{-2}{11}$

Since $x$ cannot be negative, $x$ = 22

i.e., speed of the boat in still water = 22 km/hr

40. The speed of a boat in still water is 8 kmph. If it can travel 1 km upstream in 1 hr, what time it would take to travel the same distance downstream?
A. 1 minute	B. 2 minutes
C. 3 minutes	D. 4 minutes

answer with explanation

Answer: Option D
Explanation:
Speed of the boat in still water = 8 km/hr

Speed upstream $=\frac{1}{1}$ = 1 km/hr

Speed of the stream = 8-1 = 7 km/hr

Speed downstream = (8+7) = 15 km/hr

Time taken to travel 1 km downstream $=\frac{1}{15}\text{hr =}\frac{1\times 60}{15}\text{= 4 minutes}$