1. A man can row at a speed of $$4\frac{1}{2}$$ km/hr in still water. If he takes 2 times as long to row a distance upstream as to row the same distance downstream, then the speed of stream (in km/hr) is-
a) 1
b) 1.5
c) 2
d) 2.5
Explanation:
$$\eqalign{ & {\text{Speed of man in still water , }} \cr & x{\text{ }} = {\text{ }}\frac{9}{2}km/hr{\text{ }} \cr & {\text{let speed of stream = }}y{\text{ }}km/h \cr & {\text{Downstream speed = }} {\frac{9}{2} + y} \cr & {\text{Upstream speed = }} {\frac{9}{2} - y} \cr & {\text{Accroding to questions,}} \cr & {\text{2}} \times {\frac{{{\text{Distance}}}}{{ {\frac{9}{2} + y} }}} = \frac{{{\text{Distance}}}}{{ {\frac{9}{2} - y} }} \cr & \frac{2}{{\frac{9}{2} + y}} = \frac{1}{{\frac{9}{2} - y}} \cr & \frac{{2 \times 2}}{{9 + 2y}} = \frac{2}{{9 - 2y}} \cr & \frac{2}{{9 + 2y}} = \frac{1}{{9 - 2y}} \cr & 18 - 4y = 9 + 2y \cr & 6y = 9 \cr & \Rightarrow y = \frac{9}{6} = \frac{3}{2} = 1.5\,km/h \cr} $$
2. A boat covers 24 km upstream and 36 km downstream in 6 hours, while it covers 36 km upstream and 24 km downstream in $$6\frac{1}{2}$$ hours. The speed of the current is ?
a) 1 km/hr
b) 2 km/hrs
c) 1.5 km/hrs
d) 2.5 km/hr
Explanation: let speed of boat in still water = x km/h
Speed of stream current = y km/h
$$\eqalign{ & \frac{{24}}{{x - y}} + \frac{{36}}{{x + y}} = 6h\,......\,(i) \cr & \frac{{36}}{{x - y}} + \frac{{24}}{{x + y}} = \frac{{13}}{2}h\,......\,(ii) \cr} $$
In these type of questions, make factor of 24 and 36 and choose the common values which satisfy the above equations.
$$\eqalign{ & {\text{24 = 2,3,4,6,8,}}\boxed{12} \cr & 36 = 3,4,9,\boxed{12} \cr} $$
Choose the common factor i.e. Put this value in equation (i)
$$\eqalign{ & \frac{{24}}{{x - y}} + \frac{{36}}{{12}} = 6 \cr & \frac{{24}}{{x - y}} + 3 = 6 \cr & x - y = 8 \cr & x + y = 12 \cr & x = 10\,\,\,,\,\,\,\,y = 2 \cr & {\text{Speed of the current,}} \cr & y = 2{\text{ km/h}} \cr} $$
3. A boat while dowenstream in a reiver converd a distance of 50 miles at an average speed of 60 miles per hour. While returning , because of the water resistance , it took 1 hour 15 minutes to cover the same distance What was the average speed during the whole journey?
a) 40 mph
b) 48 mph
c) 50 mph
d) 55 mph
Explanation:
$$\eqalign{ & {\text{Time taken to cover 50 miles downstream}} \cr & {\text{ = }}\left( {\frac{{50}}{{60}}} \right)hr{\text{ = }}\frac{5}{6}hr.{\text{ }} \cr & {\text{Time taken to cover 50 miles upstream}} \cr & {\text{ = 1hr 15m = 1}}\frac{1}{4}hrs = \frac{5}{4}hrs \cr & {\text{Total time taken to cover 100 miles}} \cr & {\text{ = }}\left( {\frac{5}{6} + \frac{5}{4}} \right)hrs = \frac{{25}}{{12}}hrs \cr & {\text{Average speed }} \cr & {\text{ = }}\frac{{100}}{{\left( {\frac{{25}}{{12}}} \right)}}mph \cr & = \left( {\frac{{100 \times 12}}{{25}}} \right)mph \cr & = 48mph. \cr} $$
4. A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours. Then the speed of boat in still water and the speed of current are respectively
a) 4 kmph and 3 kmph
b) 4.5 kmph and 0.5 kmph
c) 4 kmph and 2 kmph
d) 5 kmph and 2 kmph
Explanation:
$$\eqalign{ & {\text{Upstream speed, U}} \cr & {\text{ = }}\frac{{24}}{6} = 4\,km/h \cr & {\text{Downstream speed , D}} \cr & {\text{ = }}\frac{{20}}{4} = 5\,km/h \cr & {\text{Speed of boat in still water , }}x \cr & = \frac{{{\text{D + U}}}}{2} = \frac{9}{2} = 4.5\,km/h \cr & {\text{Speed of water current, }}y \cr & = \frac{{{\text{D - U}}}}{2} = \frac{1}{2} = 0.5\,km/h \cr} $$
5. A man can row 6 km/hr in still water. If the speed of the current is 2 km/hr he takes 4 hours more in upstream than the downstream. The distance is?
a) 30 km
b) 24 km
c) 20 km
d) 32 km
Explanation:
Speed of man in still water, x = 6 km/h
Speed of current, y = 2 km/h
Let distance = M
Upstream time = Downstream time + 4
$$\eqalign{ & \frac{M}{4} = \frac{M}{8} + 4 \cr & \frac{M}{4} = \frac{{M + 32}}{8} \cr & M = 32 \cr & {\text{Distance = 32 }}km \cr} $$
6. If the speed of a boat in still water is 20km/hr and the speed of the current is 5km, then the time taken by the boat to travel 100 km with the current is?
a) 2 hours
b) 3 hours
c) 4 hours
d) 7 hours
Explanation: Relative speed = 20 + 5 = 25 km/hr
Time = $$\frac{{100}}{{25}}$$ = 4 hours
7. A man takes 2.2 times as long to row a distance upstream as to row the same distance downstream. If he can row 55 km downstream in 2 hour 30 minutes, what is the speed of the boat in the still water?
a) 40 km/h
b) 8 km/h
c) 16 km/h
d) 24 km/h
Explanation:
$$\eqalign{ & {\text{Speed of the boat in downstream }} \cr & {\text{ = }}\frac{{55}}{{2.5}} = \frac{{55 \times 10}}{{25}} = 22\,km/hr \cr & {\text{Then, speed of the boat in upstream}} \cr & {\text{ = }}\frac{{22}}{{2.2}} = \frac{{22 \times 10}}{{22}} = 10\,km/hr \cr & {\text{Speed of the boat in still water}} \cr & {\text{ = }}\frac{{22 + 10}}{2} = 16\,km/hr \cr} $$
8. The speed of the boat in still water is 5 times that of current, it takes 1.1 hour to row to point B from point A downstream. The distance between point A and point B is 13.2 km. How much distance (in km) will it cover in 312 minutes upstrem?
a) 43.2
b) 48
c) 41.6
d) 44.8
Explanation: Let the speed of the current be x kmph
Then speed of the boat in still water = 5x
$$\eqalign{ & {\text{Downstream speed}} \cr & {\text{ = }}\left( {5x + x} \right) = 6x\,kmph \cr & {\text{Upstream speed}} \cr & {\text{ = }}\left( {5x - x} \right) = 4x\,kmph \cr & {\text{Now, }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{13}}{\text{.2km}}\,\,\,\, \cr & {\text{A}}\overline {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} {\text{B}} \cr & {\text{According to question,}} \cr & {\text{1}}{\text{.1}} \times {\text{6}}x = 13.2 \cr & \Rightarrow 6.6x = 13.2 \cr & \Rightarrow x = \frac{{13.2}}{{6.6}} \cr & x = 2\,kmph \cr & {\text{Upstream speed}} \cr & {\text{ = 4}}x = 4 \times 2 = 8\,kmph \cr & {\text{312 minutes}}\, \cr & = 5\frac{1}{5}\,hours \cr & = \frac{{26}}{5}\,hours \cr & {\text{Required distance travelled upstream}} \cr & {\text{ = Speed }} \times {\text{Time}} \cr & {\text{ = 8}} \times \frac{{26}}{5} = 41.6\,km \cr} $$
9. A boat can tarvel 36 km upstream in 5 hours. If the speed of the stream is 2.4 kmph, how much time will the boat take to cover a distance of 78 km downstream?(in hours)
a) 5 hours
b) 6.5 hours
c) 5.5 hours
d) 8 hours
Explanation: Distance covered by a boat in 5 hours = 36 km
Rate upstream of boat = $$\frac{{36}}{5}$$ = 7.2 kmph
Speed of the stream = 2.4 kmph
Speed of the boat in still water
= (7.2 + 2.4) kmph
= 9.6 kmph
Rate downstream of the boat
= (9.6 + 2.4) kmph
= 12 kmph
Time taken in covering 78 km distance
= $$\frac{{78}}{{12}}$$
= 6.5 hours
10. A man can row upstream at 12km/hr and downstream at 18 km/hr. The man rowing speed in still water is?
a) 15 km/hr
b) 5 km/hr
c) 25 km/h
d) 10 km/h
Explanation: Speed of boat in still water = $$\frac{{x + y}}{2}$$
Where (x = downstream speed) and (y = upstream speed)
Boat's speed
$$\eqalign{ & {\text{ = }}\frac{{18 + 12}}{2} \cr & = \frac{{30}}{2} \cr & = 15\,km/hr \cr} $$