A man can row upstream at $10$ kmph and downstream at $18$ kmph. Find the man's rate in still water? [Indian Railways Gr. 'D' Exam, 2014]

### Concept & Basic Averages The speed of a boat or person in still water is the arithmetic mean of their upstream and downstream speeds. $$ \text{Still Water Speed} = \frac{\text{Downstream Speed} + \text{Upstream Speed}}{2} $$ ### Step-by-Step Solution * Identify the given speeds: Downstream speed ($D$) = $18$ kmph, Upstream speed ($U$) = $10$ kmph. * Apply the formula for rate in still water: $\frac{18 + 10}{2}$. * Calculate the sum: $18 + 10 = 28$. * Divide by $2$: $\frac{28}{2} = 14$ kmph. ### Exam Strategy & Shortcut This is a direct formula application. Mentally add the two speeds and halve the result for an instant answer. ### Common Pitfall Subtracting the values instead of adding them, which would mistakenly give the speed of the current ($4$ kmph) instead of the still water speed. ### Final Answer Therefore, the correct answer is **(a) 14 kmph**.