Problems on Boats and Streams(Set 2) - Solved Examples

Problems on Boats and Streams(Set 1) - Solved Examples

11. A boat running downstream covers a distance of 22 km in 4 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?
A. 5 kmph	B. 4.95 kmph
C. 4.75 kmph	D. 4.65

answer with explanation

Answer: Option B
Explanation:
Speed downstream $=\frac{22}{4}\text{= 5.5 kmph}$

Speed upstream $=\frac{22}{5}\text{= 4.4 kmph}$

Speed of the boat in still water $=\frac{5.5+4.4}{2}\text{= 4.95 kmph}$

12. A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:
A. 3 : 1	B. 1 : 3
C. 1 : 2	D. 2 : 1

answer with explanation

Answer: Option A
Explanation:
Let speed upstream = $x$
Then, speed downstream = 2x

Speed in still water $=\frac{2x+x}{2}=\frac{3x}{2}$

Speed of the stream $=\frac{2x-x}{2}=\frac{x}{2}$

Speed in still water : Speed of the stream $=\frac{3x}{2}:\frac{x}{2}=3:1$

13. A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
A. 3.2 km	B. 3 km
C. 2.4 km	D. 3.6 km

answer with explanation

Answer: Option C
Explanation:
Speed in still water = 5 kmph
Speed of the current = 1 kmph

Speed downstream = (5+1) = 6 kmph
Speed upstream = (5-1) = 4 kmph

Let the required distance be $x$ km
Total time taken = 1 hour

$\Rightarrow \frac{x}{6}+\frac{x}{4}=1\Rightarrow 2x+3x=12\Rightarrow 5x=12\Rightarrow x=2.4\text{km}$

14. A man can row three-quarters of a kilometre against the stream in 111⁄4 minutes and down the stream in 71⁄2minutes. The speed (in km/hr) of the man in still water is:
A. 4 kmph	B. 5 kmph
C. 6 kmph	D. 8 kmph

answer with explanation

Answer: Option B
Explanation:
Distance $=\frac{3}{4}$ km

Time taken to travel upstream $=11\frac{1}{4}$ minutes $=\frac{45}{4}$ minutes
$=\frac{45}{4\times 60}$ hours $=\frac{3}{16}$ hours

Speed upstream $=\frac{\text{Distance}}{\text{Time}}=\frac{\left(\frac{3}{4}\right)}{\left(\frac{3}{16}\right)}=\text{4 km/hr}$

Time taken to travel downstream $=7\frac{1}{2}$ minutes $=\frac{15}{2}$ minutes
$=\frac{15}{2\times 60}$ hours $=\frac{1}{8}$ hours

Speed downstream $=\frac{\text{Distance}}{\text{Time}}=\frac{\left(\frac{3}{4}\right)}{\left(\frac{1}{8}\right)}=\text{6 km/hr}$

Rate in still water $=\frac{6+4}{2}=\frac{10}{2}=5\text{kmph}$

15. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:
A. 4 mph	B. 2.5 mph
C. 3 mph	D. 2 mph

answer with explanation

Answer: Option D
Explanation:
Speed of the boat in still water = 10 mph
Let speed of the stream be $x$ mph

Then, speed downstream $=(10+x)$ mph
speed upstream $=(10-x)$ mph

Time taken to travel 36 miles upstream - Time taken to travel 36 miles downstream $=\frac{90}{60}$ hours

$\Rightarrow \frac{36}{10-x}-\frac{36}{10+x}=\frac{3}{2}\Rightarrow \frac{12}{10-x}-\frac{12}{10+x}=\frac{1}{2}$

$\Rightarrow 24(10+x)-24(10-x)$ $=(10+x)(10-x)$

$\Rightarrow 240+24x-240+24x$ $=(100-x^2)$

$\Rightarrow 48x=100-x^2\Rightarrow x^2+48x-100=0\Rightarrow (x+50)(x-2)=0\Rightarrow x\text{= -50 or 2}$

Since $x$ can not be negative, $x$ = 2 mph

16. Tap 'A' can fill the tank completely in 6 hrs while tap 'B' can empty it by 12 hrs. By mistake, the person forgot to close the tap 'B', As a result, both the taps, remained open. After 4 hrs, the person realized the mistake and immediately closed the tap 'B'. In how much time now onwards, would the tank be full?
A. 2 hours	B. 4 hours
C. 5 hours	D. 1 hour

answer with explanation

Answer: Option B
Explanation:
Tap A can fill the tank completely in 6 hours
=> In 1 hour, Tap A can fill $\frac{1}{6}$ of the tank

Tap B can empty the tank completely in 12 hours
=> In 1 hour, Tap B can empty $\frac{1}{12}$ of the tank

i.e., In one hour, Tank A and B together can effectively fill $(\frac{1}{6}-\frac{1}{12})=\frac{1}{12}$ of the tank

=> In 4 hours, Tank A and B can effectively fill $\frac{1}{12}\times 4=\frac{1}{3}$ of the tank.

Time taken to fill the remaining $(1-\frac{1}{3})=\frac{2}{3}$ of the tank $=\frac{\left(\frac{2}{3}\right)}{\left(\frac{1}{6}\right)}$ = 4 hours

17. A Cistern is filled by pipe A in 8 hrs and the full Cistern can be leaked out by an exhaust pipe B in 12 hrs. If both the pipes are opened in what time the Cistern is full?
A. 12 hrs	B. 24 hrs
C. 16 hrs	D. 32 hrs

answer with explanation

Answer: Option B
Explanation:
Pipe A can fill $\frac{1}{8}$ of the cistern in 1 hour.

Pipe B can empty $\frac{1}{12}$ of the cistern in 1 hour

Both Pipe A and B together can effectively fill $\frac{1}{8}-\frac{1}{12}=\frac{1}{24}$ of the cistern in 1 hour

i.e, the cistern will be full in 24 hrs.

18. In a river flowing at 2 km/hr, a boat travels 32 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time.
A. 10 hours	B. 12 hours
C. 14 hours	D. 16 hours

answer with explanation

Answer: Option B
Explanation:
Solution 1

speed of the boat = 6 km/hr

Speed downstream = (6+2) = 8 km/hr
Speed upstream = (6-2) = 4 km/hr

Distance travelled downstream = Distance travelled upstream = 32 km

Total time taken
= Time taken downstream + Time taken upstream
$=\frac{32}{8}+\frac{32}{4}=\frac{32}{8}+\frac{64}{8}=\frac{96}{8}$ = 12 hr

---

Solution 2

A man can row a boat in still water at $x$ km/hr in a stream flowing at $y$ km/hr. If it takes him $t$ hours to row a place and come back, then the distance between the two places

$=\frac{t(x^2-y^2)}{2x}\text{km}$

[Read more ...]

$x$ = 6 km/hr
$y$ = 2 km/hr
distance = 32 km

As per the formula, we have
$\text{32}=\frac{t(6^2-2^2)}{2\times 6}\Rightarrow 32=\frac{32t}{12}\Rightarrow t=12\text{hr}$

19. Two pipes A and B can fill a tank in 10 hrs and 40 hrs respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
A. 8 hours	B. 6 hours
C. 4 hours	D. 2 hours

answer with explanation

Answer: Option A
Explanation:
Pipe A can fill $\frac{1}{10}$ of the tank in 1 hr

Pipe B can fill $\frac{1}{40}$ of the tank in 1 hr

Pipe A and B together can fill $\frac{1}{10}+\frac{1}{40}=\frac{1}{8}$ of the tank in 1 hr

i.e., Pipe A and B together can fill the tank in 8 hours

20. A boat covers a certain distance downstream in 4 hours but takes 6 hours to return upstream to the starting point. If the speed of the stream be 3 km/hr, find the speed of the boat in still water
A. 15 km/hr	B. 12 km/hr
C. 13 km/hr	D. 14 km/hr

answer with explanation

Answer: Option A
Explanation:
Solution 1

Let the speed of the water in still water = $x$
Given that speed of the stream = 3 kmph

Speed downstream $=(x+3)$ kmph
Speed upstream $=(x-3)$ kmph

He travels a certain distance downstream in 4 hour and come back in 6 hour.
ie, distance travelled downstream in 4 hour = distance travelled upstream in 6 hour

since distance = speed × time, we have
$(x+3)4=(x-3)6\Rightarrow (x+3)2=(x-3)3\Rightarrow 2x+6=3x-9\Rightarrow x=6+9=15\text{kmph}$

---

Solution 2

A man rows a certain distance downstream in $t_1$ hours and returns the same distance upstream in $t_2$ hours. If the speed of the stream is $y$ km/hr, then the speed of the man in still water

$=y\left(\frac{t_2+t_1}{t_2-t_1}\right)\text{km/hr}$

[Read more ...]

$t_1$ = 4 hour
$t_2$ = 6 hour
$y$ = 3 km/hr

By using the the above formula, Speed of the boat in still water
$=y\left(\frac{t_2+t_1}{t_2-t_1}\right)=3\left(\frac{6+4}{6-4}\right)\text{= 15 km/hr}$