The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to original point in 4 hours 30 minutes. Find speed of stream.

Let speed of stream be x km/hr.

Upstream speed = (15 - x) km/hr

Downstream speed = (15 + x) km/hr

Time taken to travel 30 km upstream = $\dfrac{30}{15- x}$ hours

Time taken to travel 30 km downstream = $\dfrac{30}{15 + x}$ hours

Given,

$\dfrac{30}{15- x} + \dfrac{30}{15 + x} = \dfrac{270}{60} \\[1em] \Rightarrow \dfrac{30(15 + x) + 30(15 - x)}{(15 - x)(15 + x)} = \dfrac{9}{2} \\[1em] \Rightarrow \dfrac{450 + 30x + 450 - 30x}{225 + 15x - 15x - x^2} = \dfrac{9}{2} \\[1em] \Rightarrow \dfrac{900}{225 - x^2} = \dfrac{9}{2} \\[1em] \Rightarrow 1800 = 9(225 - x^2) \\[1em] \Rightarrow 1800 = 2025 - 9x^2 \\[1em] \Rightarrow 9x^2 + 1800 - 2025 = 0 \\[1em] \Rightarrow 9x^2 - 225 = 0 \\[1em] \Rightarrow 9x^2 = 225 \\[1em] \Rightarrow x^2 = \dfrac{225}{9} = 25 \\[1em] \Rightarrow x = \sqrt{25} = \pm 5.$

Since speed cannot be negative,

∴ x ≠ -5.

Hence, speed of stream = 5 km/hr.