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What will be Raj’s speed in still water as well as speed of the river, if he can go downstream at 18 km/hr and upstream at 10 km/hr?

  • A.Raj = 10 km/hr ; River = 5 km/hr
  • B.Raj = 14 km/hr ; River = 4 km/hr
  • C.Raj = 28 km/hr ; River = 8 km/hr
  • D.Raj = 8 km/hr ; River = 28 km/hr

Answer: B

Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then

\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]

\[ b = \frac{18 + 10}{2} = 14 \text{ km/h} \]

\[ r = \frac{18 - 10}{2} = 4 \text{ km/h} \]

Checking: \( 14 + 4 = 18 \) downstream and \( 14 - 4 = 10 \) upstream. The 28 and 8 option forgets to halve; the still-water speed must always lie between the two given speeds.

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