Discussion
Consider statements A and B given below and decide whether they are enough to find the time needed for covering same distance downstream as upstream if a boat travels 48 kms upstream in 6 hours.
Statement A - Boat’s speed in still water is 10 km/hr
Statement B - Current speed is 2 km/hr
Answer: B
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
The upstream trip already gives one speed outright:
\[ b - r = \frac{48}{6} = 8 \text{ km/h} \]
With statement A (\( b = 10 \)): \( r = 2 \), so \( b + r = 12 \) and the downstream time is \( \tfrac{48}{12} = 4 \) hours.
With statement B (\( r = 2 \)): \( b = 10 \), giving the same \( b + r = 12 \) and the same 4 hours.
Each statement alone completes the pair, so either one is sufficient. Once \( b - r \) is known, any single further fact about \( b \) or \( r \) determines the other - which is exactly the situation this data-sufficiency format is testing.
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