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 :

### Concept & Formula Total time for a round trip involving a stream is the sum of the time taken to travel downstream and the time taken to travel upstream. $$ \text{Total Time} = \frac{d}{B + S} + \frac{d}{B - S} $$ Where $d$ is the one-way distance, $B$ is boat speed, and $S$ is stream speed. ### Step-by-Step Solution * **Given:** Boat speed ($B$) = $9$ kmph, Stream speed ($S$) = $1.5$ kmph, Distance ($d$) = $105$ km. * Calculate Downstream speed ($D$): $D = B + S = 9 + 1.5 = 10.5 \text{ kmph}$. * Calculate Upstream speed ($U$): $U = B - S = 9 - 1.5 = 7.5 \text{ kmph}$. * Calculate time for downstream journey: $T_{\text{down}} = \frac{105}{10.5} = 10 \text{ hours}$. * Calculate time for upstream journey: $T_{\text{up}} = \frac{105}{7.5} = 14 \text{ hours}$. * Calculate total time: $\text{Total Time} = 10 + 14 = 24 \text{ hours}$. ### Exam Strategy & Shortcut Calculate speeds: $10.5 = \frac{21}{2}$ and $7.5 = \frac{15}{2}$. Total time $= 105 \times \left(\frac{2}{21}\right) + 105 \times \left(\frac{2}{15}\right) = 10 + 14 = 24$. Using fractions can be faster than dividing by decimals. ### Common Pitfall Forgetting that a "round trip" consists of exactly one downstream leg and one upstream leg, and erroneously applying an average speed formula incorrectly. ### Final Answer Therefore, the correct answer is **24 hours**.