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 $v$ = speed of boat in still water, $s$ = speed of stream
Upstream speed = $v - s$, Downstream speed = $v + s$
Equations:
$\frac{32}{v-s} + \frac{36}{v+s} = 7$
$\frac{40}{v-s} + \frac{48}{v+s} = 9$
Let $p = v - s$, $q = v + s$
$\frac{32}{p} + \frac{36}{q} = 7$
$\frac{40}{p} + \frac{48}{q} = 9$
$\frac{40}{p} + \frac{48}{q} - \frac{40}{p} - \frac{45}{q} = 9 - 8.75 \Rightarrow \frac{3}{q} = 0.25 \Rightarrow q = 12$
$\frac{32}{p} + \frac{36}{12} = 7 \Rightarrow \frac{32}{p} + 3 = 7 \Rightarrow \frac{32}{p} = 4 \Rightarrow p = 8$
$v - s = 8$, $v + s = 12 \Rightarrow 2v = 20 \Rightarrow v = 10$ km/hr
Answer: 10 km/hr