(d) 2 km/hr
Let the speed of the stream be x km/hr.
Speed of boat in still water = 10 km/hr
∴ Speed of boat downstream = (10 + x) km/hr
Speed of boat upstream = (10 – x) km/hr
Given, \(\frac{36}{(10-x)}-\frac{36}{(10+x)}=\frac{90}{60}\)
⇒ \(\frac{36(10+x)-36(10-x)}{(10-x)(10+x)}=\frac32\)
⇒ \(\frac{72x}{100-x^2}=\frac32\) ⇒ 144x = 300 – 3x2
⇒ 3x2 + 144x – 300 = 0
⇒ 3x2 + 150x – 6x – 300 = 0
⇒ 3x(x + 50) –6(x + 50) = 0
⇒ (3x – 6) (x + 50) = 0
⇒ x = 2 or –50.
Since speed is not negative, x = 2 km/hr.