1. A boat can travel with a speed of 13 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) 2 hours
b) 3 hours
c) 4 hours
d) 5 hours
Explanation: Speed downstream
= (13 + 4) km/hr
= 17 km/hr
Time taken to travel 68 km downstream
= $$\frac{{68}}{{17}}$$ hours
= 4 hours
2. The ages of Shakti and Kanti are in the ratio of 8 : 7 respectively. After 10 years, the ratio of their ages will be 13 : 12. What is the difference between their ages ?
a) 8.5 km/hr
b) 9 km/hr
c) 10 km/hr
d) 12.5 km/hr
Explanation: Man's rate in still water
= (15 - 2.5) km/hr
= 12.5 km/hr.
Man's rate against the current
= (12.5 - 2.5) km/hr
= 10 km/hr.
3. A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
a) 2 : 1
b) 3 : 2
c) 8 : 3
d) None of these
Explanation: Let the man's rate upstream be x kmph and that downstream be y kmph.
Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.
$$\eqalign{ & {x \times 8\frac{4}{5}} = {y \times 4} \cr & \frac{{44}}{5}x = 4y \cr & y = \frac{{11}}{5}x \cr & {\text{Required}}\,{\text{ratio}} \cr & = {\frac{{y + x}}{2}} : {\frac{{y - x}}{2}} \cr & = \left( {\frac{{16x}}{5} \times \frac{1}{2}} \right):\left( {\frac{{6x}}{5} \times \frac{1}{2}} \right) \cr & = \frac{8}{5}:\frac{3}{5} \cr & = 8:3 \cr} $$
4. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
a) 4 km/hr
b) 5 km/hr
c) 6 km/hr
d) 10 km/hr
Explanation: Let the speed of the stream be x km/hr
Speed downstream = (15 + x) km/hr
Speed upstream = (15 - x) km/hr
$$\eqalign{ & \frac{{30}}{{ {15 + x} }} + \frac{{30}}{{ {15 - x} }} = 4\frac{1}{2} \cr & \frac{{900}}{{225 - {x^2}}} = \frac{9}{2} \cr & 9{x^2} = 225 \cr & {x^2} = 25 \cr & x = 5\,km/hr \cr} $$
5. In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
a) 3 kmph
b) 5 kmph
c) 8 kmph
d) 9 kmphr
Explanation: Speed in still water
= $$\frac{1}{2}$$(11 + 5) kmph
= 8 kmph.
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) 40 minutes
b) 1 hour
c) 1 hr 15 min
d) 1 hr 30 min
Explanation:
$$\eqalign{ & {\text{Rate}}\,{\text{downstream}} \cr & = \left( {\frac{1}{{10}} \times 60} \right)km/hr = 6\,km/hr \cr & {\text{Rate}}\,{\text{upstream}} = 2\,km/hr \cr & {\text{Speed}}\,{\text{in}}\,{\text{still}}\,{\text{water}} \cr & = \frac{1}{2}\left( {6 + 2} \right)km/hr = 4\,km/hr \cr & {\text{Required}}\,{\text{time}} = {\frac{5}{4}} \,hrs \cr & = 1\frac{1}{4}hrs \cr & = 1\,hr\,15\,\min . \cr} $$
7. A man can row three-quarters of a kilometer against the stream in $$11\frac{1}{4}$$ minutes and down the stream in $$7\frac{1}{2}$$ minutes. The speed (in km/hr) of the man in still water is:
a) 2
b) 3
c) 4
d) 5
Explanation: We can write three - quarters of a kilometer as 750 meters and $$11\frac{1}{4}$$ minutes as 675 seconds
$$\eqalign{ & {\text{Rate}}\,{\text{upstream}} \cr & = {\frac{{750}}{{675}}} m/\sec = \frac{{10}}{9}m/\sec \cr & {\text{Rate}}\,{\text{downstream}} \cr & = {\frac{{750}}{{450}}} m/\sec = \frac{5}{3}m/\sec \cr & {\text{Rate}}\,{\text{in}}\,{\text{still}}\,{\text{water}} = \frac{1}{2}\left( {\frac{{10}}{9} + \frac{5}{3}} \right)m/\sec \cr & = \frac{{25}}{{18}}\,m/\sec \cr & = \left( {\frac{{25}}{{18}} \times \frac{{18}}{5}} \right)km/hr \cr & = 5\,km/hr \cr} $$
8. Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. 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) 16 hours
b) 18 hours
c) 20 hours
d) 24 hours
Explanation: Speed upstream = 7.5 kmph
Speed downstream = 10.5 kmph
Total time taken
= $$\left( {\frac{{105}}{{7.5}} + \frac{{105}}{{10.5}}} \right)$$ hours
= 24 hours
9. 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) 2 : 1
b) 3 : 1
c) 3 : 2
d) 4 : 3
Explanation: Let man's rate upstream be x kmph
Then, his rate downstream = 2x kmph
(speed in still water) : (Speed of stream)
$$\eqalign{ & = {\frac{{2x + x}}{2}} : {\frac{{2x - x}}{2}} \cr & = \frac{{3x}}{2}:\frac{x}{2} \cr & = 3:1 \cr} $$.
10. A man rows to a place 48 km distant and come 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/hr
b) 1.5 km/hr
c) 2 km/hr
d) 2.5 km/hr
Explanation: Suppose he move 4 km downstream in x hours
Speed downstream = $$\frac{4}{x}$$ km/hr
Speed upstream = $$\frac{3}{x}$$ km/hr
$$\eqalign{ & \therefore \frac{{48}}{{\left( {4/x} \right)}} + \frac{{48}}{{\left( {3/x} \right)}} = 14\,or\,x = \frac{1}{2} \cr} $$
So, Speed downstream = 8 km/hr
Speed upstream = 6 km/hr
Rate of the stream = $$\frac{1}{2}$$(8 - 6) km/hr
= 1 km/hr