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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