A boat takes total time of 3 hours to cover a distance of 18 km down the stream and 12 km up the stream. While the same boat takes a total time of 6(1/2) hours to cover a distance of 36 km up the stream and 24 km down the stream. Then what is the speed of the boat?

Let boat speed = v, stream speed = u. Downstream speed = v+u, upstream = v-u. From first trip: 18/(v+u) + 12/(v-u) = 3. From second: 36/(v-u) + 24/(v+u) = 6.5. Noting that 36/12 = 3 and 24/18 = 4/3, we can derive that 2×(first equation) gives 36/(v+u) + 24/(v-u) = 6. Comparing with second equation, we find v-u = 20/3 and v+u = 20, so v = 10 km/hr. Option B is correct.