Correct Answer: Option A
Let:
Setting up equations:
Solving the system of equations:
Adding equations (1) and (2):
(B + C) + (B - C) = 13 + 8
2B = 21
B = 10.5 kmph
Subtracting equation (2) from (1):
(B + C) - (B - C) = 13 - 8
2C = 5
C = 2.5 kmph
Verification:
Direct formula for stream speed:
Speed of stream = ½(Downstream speed - Upstream speed)
= ½(13 - 8)
= ½ × 5
= 2.5 kmph
Bonus formula for boat speed:
Speed in still water = ½(Downstream speed + Upstream speed)
= ½(13 + 8)
= ½ × 21
= 10.5 kmph
Therefore, the answer is A) 2.5 km/hr.
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