Question

The speed of a motorboat is to that of the current of water as $36:5$. The boat goes along with the current in $5$ hours $10$ min. It will come back in

• A. $5$ hours $50$ min
• B. $6$ hours
• C. $6$ hours $50$ min
• D. $12$ hours $10$ min

Answer 1

The correct option is C $6$ hours $50$ min

Let the speed of the motorboat be $36x$ km/hr and that of the current water be $5x$ km/hr.
Speed downstream $=(36x+5x)$ km/hr $=41x$ km/hr
Speed upstream $=(36x-5x)=31x$ km/hr
Time taken to downstream $=5$ hrs $10$ min
$=$ $5\frac{10}{60}$ hrs $=\frac{31}{6}$ hrs
$\therefore$ Distance covered downstream $=$ $(41x\times \frac{31}{6})$ km
$\therefore$ Distance covered upstream $=$ $(41x\times \frac{31}{6})$ km
$\therefore$ Time taken to travel upstream $=$ $(41x\times \frac{31}{6}\times \frac{1}{31x})hrs=\frac{41}{6}hrs=6\frac{5}{6}hrs$ $=6$ hrs $50$ min