Boats And Streams - Aptitude MCQ Questions and Solutions with Explanations

Relative speed = 20 + 5 = 25 km/hr
Time = $$\frac{{100}}{{25}}$$ = 4 hours

$$\eqalign{ & {\text{Speed of the boat in downstream }} \cr & {\text{ = }}\frac{{55}}{{2.5}} = \frac{{55 \times 10}}{{25}} = 22\,km/hr \cr & {\text{Then, speed of the boat in upstream}} \cr & {\text{ = }}\frac{{22}}{{2.2}} = \frac{{22 \times 10}}{{22}} = 10\,km/hr \cr & \therefore {\text{Speed of the boat in still water}} \cr & {\text{ = }}\frac{{22 + 10}}{2} = 16\,km/hr \cr} $$

Let the speed of the current be x kmph
Then speed of the boat in still water = 5x
$$\eqalign{ & \therefore {\text{Downstream speed}} \cr & {\text{ = }}\left( {5x + x} \right) = 6x\,kmph \cr & {\text{Upstream speed}} \cr & {\text{ = }}\left( {5x - x} \right) = 4x\,kmph \cr & {\text{Now, }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{13}}{\text{.2km}}\,\,\,\, \cr & {\text{A}}\overline {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} {\text{B}} \cr & {\text{According to question,}} \cr & {\text{1}}{\text{.1}} \times {\text{6}}x = 13.2 \cr & \Rightarrow 6.6x = 13.2 \cr & \Rightarrow x = \frac{{13.2}}{{6.6}} \cr & \therefore x = 2\,kmph \cr & \therefore {\text{Upstream speed}} \cr & {\text{ = 4}}x = 4 \times 2 = 8\,kmph \cr & \therefore {\text{312 minutes}}\, \cr & = 5\frac{1}{5}\,hours \cr & = \frac{{26}}{5}\,hours \cr & \therefore {\text{Required distance travelled upstream}} \cr & {\text{ = Speed }} \times {\text{Time}} \cr & {\text{ = 8}} \times \frac{{26}}{5} = 41.6\,km \cr} $$

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

Speed of boat in still water = $$\frac{{x + y}}{2}$$
Where (x = downstream speed) and (y = upstream speed)
∴ Boat's speed
$$\eqalign{ & {\text{ = }}\frac{{18 + 12}}{2} \cr & = \frac{{30}}{2} \cr & = 15\,km/hr \cr} $$

$$\eqalign{ & {\text{P - - - - - - - - - - }}\mathop {\text{ - }}\limits_{\text{Q}} {\text{ - - - - - - - - - - R}} \cr & {\text{ < - - - - - - - 16}}{\text{.40 - - - - - - - > }} \cr & \because {\text{Time required travelling from P to R}} \cr & {\text{ = 16H 40M}} \cr & \because {\text{PQ = QR}}\left( {\because {\text{Q is mid point}}} \right){\text{ }} \cr & {\text{Required time to travel PQ}} \cr & {\text{ = }}\frac{1}{2}\left( {{\text{16H 40M}}} \right) = \,\,{\text{8H 20M}} \cr & {\text{total required time from}} \cr & {\text{P to Q + Q to P = 12H}} \cr & {\text{ = 8H 20M + Q to P = 12H}} \cr & {\text{Time Q to P}} \cr & {\text{ = 12H - 8H 20M}} \cr & {\text{ = 3H 40M}} \cr & \because \overrightarrow {{\text{QP}}} {\text{ = }}\frac{1}{2}\overrightarrow {{\text{RP}}} {\text{ }}\,\,\left( {{\text{Distance}}} \right) \cr & \therefore {\text{Required time to }}\overrightarrow {{\text{RP}}} {\text{ }} \cr & {\text{ = 2}} \times \left[ {\overrightarrow {{\text{QP}}} } \right] \cr & {\text{ = 2}}\left[ {3{\text{H 40M}}} \right]{\text{ }} \cr & {\text{ = 7 H 20M}} \cr & {\text{ = 7}}\frac{1}{3}{\text{hr}}{\text{ }} \cr} $$

Speed of boat in upstream = $$\frac{{35}}{7}$$ = 5 km/hr
Speed of boat in downstream = $$\frac{{35}}{5}$$ = 7 km/hr
Let the speed of boat x and speed of stream be y
Now,
x - y = 5
x + y = 7
$$\overline {\,2{\text{x}} = 12\,} $$
∴ x = 6 km/hr

$$\eqalign{ & {\text{Let, speed of boat}} = x \cr & {\text{Speed of stream}} = y \cr & \Rightarrow \frac{{48}}{{x + y}} + \frac{{48}}{{x - y}} = 14\,.\,.\,.\,.\,.\,\left( {\text{i}} \right) \cr & {\text{and, }}\frac{4}{{x + y}} = \frac{3}{{x - y}} \cr & \frac{{x - y}}{{x + y}} = \frac{3}{4} = \frac{6}{8} \cr & {\text{From equation }}\left( {\text{i}} \right), \cr & \frac{{48}}{8} + \frac{{48}}{6} = 14 \cr & 14 = 14\,\,\,\left( {{\text{Satisfied}}} \right) \cr & {\text{So, }}x - y = 6 \cr & \,\,\,\,\,\,\,\,\,x + y = 8 \cr & \,\,\,\,\,\overline {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,y = 1\,\,} {\text{km/hr}} \cr} $$

$$\eqalign{ & {\text{B}} + {\text{W}} = 12{\text{ km/h}} \cr & {\text{B}} - {\text{W}} = 10{\text{ km/h}} \cr & \overline {\,{\text{B}} = \frac{{22}}{2} = 11{\text{ km/h}}\,} \cr} $$

Let speed of boat is x and stream is y km/hr
According to the question
$$\eqalign{ & \frac{{25}}{{x - y}} + \frac{{39}}{{x + y}} = 8 \cr & \frac{{35}}{{x - y}} + \frac{{52}}{{x + y}} = 11 \cr} $$
By hit and trail method x = 9, y = 4 it satisfy the both equations
Speed of stream = 4 km/hr