1. A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?
a) 4 kmph
b) 6 kmph
c) 8 kmph
d) None of these
Explanation: Rate downstream
= $$\frac{{16}}{2}$$ kmph = 8 kmph
Rate upstream
= $$\frac{{16}}{4}$$ kmph = 4 kmph
Speed in still water
= $$\frac{1}{2}$$(8 + 4) kmph = 6 kmph
2.The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is:
a) 1.2 km
b) 1.8 km
c) 2.4 km
d) 3.6 km
Explanation: Speed downstream
= (15 + 3) kmph
= 18 kmph
Distance travelled
= $$\left( {18 \times \frac{{12}}{{60}}} \right)$$ km
= 3.6 km
3. 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) 2 mph
b) 2.5 mph
c) 3 mph
d) 4 mph
Explanation: Let the speed of the stream x mph.
Speed downstream = (10 + x) mph
Speed upstream = (10 - x) mph
$$\eqalign{ & \frac{{36}}{{ {10 - x} }} - \frac{{36}}{{ {10 + x} }} = \frac{{90}}{{60}} \cr & 72x \times 60 = 90\left( {100 - {x^2}} \right) \cr & {x^2} + 48x - 100 = 0 \cr & \left( {x + 50} \right)\left( {x - 2} \right) = 0 \cr & x = 2\,\text{mph} \cr} $$`
4. 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) 2.4 km
b) 2.5 km
c) 3 km
d) 3.6 km
Explanation: Speed downstream = (5 + 1) kmph = 6 kmph
Speed upstream = (5 - 1) kmph = 4 kmph
Let the required distance be x km
$$\frac{x}{6} + \frac{x}{4}$$ = 1
2x + 3x = 12
5x = 12
x = 2.4 km
5. A boat covers a certain distance downstream in 1 hour, while it comes back in $$1\frac{1}{2}$$ hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?
a) 12 kmph
b) 13 kmph
c) 14 kmph
d) 15 kmph
Explanation: Let the speed of the boat in still water be x kmph
Speed downstream = (x + 3) kmph
Speed upstream = (x - 3) kmph
$$\eqalign{ & \left( {x + 3} \right) \times 1 = \left( {x - 3} \right) \times \frac{3}{2} \cr & \Rightarrow 2x + 6 = 3x - 9 \cr & x = 15\,\text{kmph} \cr} $$.
6. The speed of a boat along the stream is 12 km/hr and against the stream is 8 km/hr. The time taken by the boat to sail 24 km in still water is?
a) 2 hrs
b) 4 hrs
c) 2.4 hr
d) 1.2 hrs
Explanation: Speed of downstream
D = 12 km/h
Speed of upstream
U = 8 km/h
Speed of boat in still water
$$\eqalign{ & = \frac{{D + U}}{2} \cr & = \frac{{20}}{2} \cr & = 10\,km/h \cr} $$
Time taken by the boat in still water
$$\eqalign{ & = \frac{{24\,km}}{{10\,km/hr}} \cr & = 2.4\,{\text{hours}} \cr} $$
7. A motorboat in still water travels at a speed of 36 km/hr. It goes 56 km upstream in 1 hour 45 monutes. The time taken by it to cover the same distance down the stream will be-
a) 1 hour 24 minutes
b) 2 hour 21 minutes
c) 2 hour 25 minutes
d) 3 hour
Explanation:
$$\eqalign{ & {\text{Speed upstream}} \cr & {\text{ = }}\left( {\frac{{56}}{{1\frac{3}{4}}}} \right)km/hr \cr & = \left( {56 \times \frac{4}{7}} \right)km/hr \cr & = 32km/hr \cr & {\text{let speed downstream be }}x{\text{ km/hr}}{\text{.}} \cr & {\text{Then speed of boat in still water }} \cr & {\text{ = }}\frac{1}{2}\left( {x + 32} \right)km/hr \cr & {\text{ }}\frac{1}{2}\left( {x + 32} \right) = 36\,\,\, \Rightarrow x = 40 \cr & {\text{Hence , required time}} \cr & {\text{ = }}\left( {\frac{{50}}{{40}}} \right)hrs \cr & = 1\frac{2}{5}hrs \cr & = 1\,{\text{hour}}\,24\operatorname{minutes} \cr} $$
8.P, Q and R are three towns on a river which flows uniformly. Q is equidistant from P and R. I row from P to Q and back in 10 hours and I can row from P to R in 4 hours. Compare the speed of my boat in still water with that of the river.
a) 4 : 3
b) 5 : 3
c) 6 : 5
d) 7 : 3
Explanation:
$$\eqalign{ & {\text{Let PQ = QR = }}x{\text{ }}km \cr & {\text{let speed downstream }} \cr & {\text{ = }}a{\text{ }}km/hr \cr & \,\,\,\,\,\,\,\,\,\, \to \,\,{\text{downstream}} \to \cr & {\text{P}}\overline {\,\,\,\,\,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Q}}\,\,\,\,\,\,\,\,\,\,\,\,\,y\,\,\,\,\,\,\,\,\,\,\,} \,{\text{R}}\,\,\,\, \cr & {\text{and speed upstream }} \cr & {\text{ = }}b{\text{ }}km/hr{\text{ }} \cr & {\text{then, }}\frac{x}{a} + \frac{x}{b} = 10 \cr & \Rightarrow x = \frac{{10ab}}{{a + b}} \cr & {\text{and }}\frac{{2x}}{a} = 4 \cr & \Rightarrow x = \frac{{4a}}{2} = 2a \cr & {\text{from (i) and (ii) we have:}} \cr & 2a = \frac{{10ab}}{{a + b}} \cr & 5b = a + b \cr & a = 4b \cr & {\text{Required ratio }} \cr & {\text{ = }}\frac{{{\text{Speed in still water}}}}{{{\text{Speed of river}}}} \cr & = \frac{{\frac{1}{2}\left( {a + b} \right)}}{{\frac{1}{2}\left( {a - b} \right)}} \cr & = \frac{{\left( {a + b} \right)}}{{\left( {a - b} \right)}} \cr & = \frac{{4b + b}}{{4b - b}} \cr & = \frac{5}{3} \cr} $$
9. A boat moves downstream at the rate of 1 km in $${\text{7}}\frac{1}{2}$$ minutes and upstream at the rate of 5 km an hour. What is the speed of the boat in the still water?
a) 8 km/hour
b) $${\text{6}}\frac{1}{2}$$ km/hour
c) 4 km/hour
d) $${\text{3}}\frac{1}{2}$$ km/hour
Explanation: Rate downstream of boat
$$\eqalign{ & {\text{ = }}\left( {\frac{1}{{\frac{{15}}{{2 \times 60}}}}} \right)\,{\text{kmph}} \cr & = \frac{{2 \times 60}}{{15}}\,{\text{kmph}} \cr & = 8\,{\text{kmph}} \cr} $$
Rate downstream of boat = 5 kmph
Speed of boat in still water = $$\frac{1}{2}$$ (Rate downstream + Rate upstream)
$$\eqalign{ & = \frac{1}{2}\left( {8 + 5} \right) \cr & = \frac{{13}}{2} \cr & = 6\frac{1}{2}\,{\text{kmph}} \cr} $$
10. A boat takes half time in moving a certain distance downstream than upstream. The ratio of the speed of the boat in still water and that of the current is?
a) 2 : 1
b) 4 : 3
c) 1 : 2
d) 3 : 1
Explanation: Let the speed of boat in still water = x km/hr,
and Speed of current = y km/hr
Rate downstream = (x + y) km/hr, and Rate upstream = (x – y) km/hr
Distance = Speed × Time
$$\eqalign{ & \left( {x - y} \right) \times 2t = \left( {x + y} \right) \times t \cr & 2x - 2y = x + y \cr & 2x - x = 2y + y \cr & x = 3y \cr & \Rightarrow \frac{x}{y} = \frac{3}{1} = 3:1 \cr} $$