A person rows a boat 10 kms along the stream in 30 minutes and returns to the starting point in 40 minutes. The speed of the stream is:

A person is rowing a boat:

• With the stream (downstream) → Takes 30 minutes to go 10 km
• Against the stream (upstream) → Takes 40 minutes to return the same 10 km

When rowing a boat:

• Downstream (with stream) = Boat's speed + Stream's speed
• Upstream (against stream) = Boat's speed - Stream's speed

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Convert time to hours:

30 minutes $= \dfrac{30}{60} = 0.5$ hours

40 minutes $= \dfrac{40}{60} = \dfrac{2}{3}$ hours

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Speed $= \dfrac{\text{Distance}}{\text{Time}}$

Downstream speed $= \dfrac{10}{0.5}$

$= 20$ km/h

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Upstream speed $= \dfrac{10}{\frac{2}{3}}$

$= 10 \times \dfrac{3}{2}$

$= 15$ km/h

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Let:

• $b$ = boat's speed in still water
• $s$ = stream's speed

Downstream: $b + s = 20$ ... (Equation 1)

Upstream: $b - s = 15$ ... (Equation 2)

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Subtracting Equation 2 from Equation 1:

$(b + s) - (b - s) = 20 - 15$

$b + s - b + s = 5$

$2s = 5$

$s = 2.5$ km/h

Therefore, the speed of the stream is 2.5 km/h.