If a person goes 20 km downstream in 5 hours and returns against the stream in 15 hours, then the speed of the stream in km/hr is :

$\frac{4}{3}$

The correct answer is Option (3) → $\frac{4}{3}$

B be the speed of the boat

S be the speed of the stream

Downstream Speed = B + S

$\frac{20}{B+S}=5$

$B+S=4$   ...(1)

Upstream Speed = B - S

$\frac{20}{B-S}=5$

$B-S=\frac{20}{15}=\frac{4}{3}$   ...(2)

Adding (1) and (2)

$(B+S)+(B-S)=4+\frac{4}{3}$

$2B=\frac{12+4}{3}=\frac{16}{3}$

$B=\frac{8}{3}$

Substituting B in (1)

$\frac{8}{3}+S=4$

$S=4-\frac{8}{3}=\frac{12-8}{3}=\frac{4}{3}$