Question : A boat takes half the time to move a certain distance downstream than upstream. The ratio of the speed of the boat in still water to that of the current is:
Option 1: $2:1$
Option 2: $1:2$
Option 3: $4:3$
Option 4: $3:1$
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Correct Answer: $3:1$
Solution : Given: A boat takes half the time to move a certain distance downstream than upstream. Use the given formula, Time × Speed = Distance Also, boat speed in still water is $p$ km/hr. Current speed = $q$ km/hr The downstream speed is $(p + q)$ km/hr. The upstream speed is $(p -q)$ km/hr. According to the question, $(p-q)\times2t = (p+q)\times t$ ⇒ $2p-2q= p +q$ ⇒ $2p-p= 2q+ q$ ⇒ $p= 3q$ ⇒ $\frac{p}{q}=\frac{3}{1}$ Hence, the correct answer is $3:1$.
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