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The speed of a motor-boat is that of the current of water as 36:5. The boat goes along with the current in 5 hours 10 minutes. It will come back in:
Answer & Solution
Correct Answer:
Option
C
Let the speed of the motor boat = 36x kmph and speed of current = 5x kmph.
The boat goes along with the current in 5 hours 10 minutes = $$\frac{{31}}{6}$$ hour $$\eqalign{ & {\text{Hence, Distance}} \cr & = {\frac{{31}}{6}} \times \left( {36x + 5x} \right) \cr & = \frac{{41x + 31}}{6}\,km \cr & {\text{Speed of boat upstream}} \cr & = 36x + 5x = 31x\,{\text{kmph}} \cr & {\text{Hence, time taken to come back}} \cr & = {\frac{{ {41x \times {\frac{{31}}{6}} } }}{{31x}}} \cr & = \frac{{41}}{6}\,{\text{hours}} \cr & = 6\,{\text{hours}}\,\,50\,{\text{minutes}} \cr} $$
The boat goes along with the current in 5 hours 10 minutes = $$\frac{{31}}{6}$$ hour $$\eqalign{ & {\text{Hence, Distance}} \cr & = {\frac{{31}}{6}} \times \left( {36x + 5x} \right) \cr & = \frac{{41x + 31}}{6}\,km \cr & {\text{Speed of boat upstream}} \cr & = 36x + 5x = 31x\,{\text{kmph}} \cr & {\text{Hence, time taken to come back}} \cr & = {\frac{{ {41x \times {\frac{{31}}{6}} } }}{{31x}}} \cr & = \frac{{41}}{6}\,{\text{hours}} \cr & = 6\,{\text{hours}}\,\,50\,{\text{minutes}} \cr} $$
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LoginD=st
t=D/s
where, D=(41x+31)/6