If a man goes 18 km downstream in 4 hours and returns against the stream in 12 hours, then the speed of the stream in km/hr is

### Concept & Formula Calculate the individual speeds using $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$. The speed of the stream is half the difference between the downstream and upstream speeds. $$ \text{Stream Speed} = \frac{\text{Downstream Speed} - \text{Upstream Speed}}{2} $$ ### Step-by-Step Solution - Downstream speed $u = \frac{18 \text{ km}}{4 \text{ hours}} = 4.5 \text{ km/hr}$. - Upstream speed $v = \frac{18 \text{ km}}{12 \text{ hours}} = 1.5 \text{ km/hr}$. - Apply the stream speed formula: $$ \text{Speed of Stream} = \frac{4.5 - 1.5}{2} = \frac{3}{2} = 1.5 \text{ km/hr} $$ ### Exam Strategy & Shortcut Calculate speeds using mental math: $18 / 4 = 4.5$ and $18 / 12 = 1.5$. Their difference is 3, and half of 3 is 1.5. ### Common Pitfall Dividing total distance by total time to find an average speed, which is irrelevant for finding the speed of the stream. ### Final Answer Therefore, the correct answer is **1.5**.