A boat covers 32 km upstream and 36 km downstream in 7 hours. Also, it covers 40 km upstream and 48 km downstream in 9 hours. The speed of the boat in still water is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 10 km/hr
Let the upstream speed be u km/hr and the downstream speed be v km/hr. Time = distance ÷ speed, so
\( \displaystyle \frac{32}{u} + \frac{36}{v} = 7 \)
\( \displaystyle \frac{40}{u} + \frac{48}{v} = 9 \)
Put \(p = \frac{1}{u}\) and \(q = \frac{1}{v}\):
\( 32p + 36q = 7 \)
\( 40p + 48q = 9 \)
Multiplying the first equation by 5 and the second by 4:
\( 160p + 180q = 35 \)
\( 160p + 192q = 36 \)
\( \displaystyle 12q = 1,\quad q = \frac{1}{12},\quad v = 12 \)
\( \displaystyle 32p + 3 = 7,\quad p = \frac{1}{8},\quad u = 8 \)
The speed in still water is the average of the downstream and upstream speeds:
\( \displaystyle \frac{12 + 8}{2} = 10 \text{ km/hr} \)
CBSE Applied Mathematics (Class XII):
Boats and Streams
