Question : A boat goes 4 km upstream and 4 km downstream in an hour. The same boat goes 5 km downstream and 3 km upstream in 55 minutes. What is the speed (in km/hr) of the boat in still water?
Option 1: 6.5
Option 2: 7.75
Option 3: 9
Option 4: 10.5
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Correct Answer: 9
Solution : Let the speed of the boat in still water be $a$ km/hr and the speed of water be $b$ km/hr. Speed in downstream = $a+b$ Speed in upstream = $a-b$ As per the first given condition: $⇒ \frac{4}{(a-b)}+\frac{4}{(a+b)}=1$ Let $\frac{1}{(a-b)}=x$ and $\frac{1}{(a+b)}=y$ $⇒4x+4y=1$ $⇒ x+y =\frac{1}{4} $ --------------------------(1) As per the second given condition: $⇒\frac{3}{(a-b)}+\frac{5}{(a+b)}=\frac{55}{60}$ $⇒3x+5y=\frac{11}{12}$ By putting the value of $y$ from equation (1) we get: $⇒3x+5(\frac{1}{4}-x)=\frac{11}{12}$ $⇒2x=\frac{5}{4}-\frac{11}{12}$ $⇒x=\frac{1}{6}⇒(a-b)=6$ ----------------------------(2) By putting the value of $x$ in equation (1) $⇒y=\frac{1}{4}-\frac{1}{6}$ $⇒y=\frac{1}{12}⇒(a+b)=$ 12 --------------------(3) From equation (2) and (3), $⇒2a= 18⇒a= 9$ The speed of the boat in still water is 9 km/hr. Hence, the correct answer is 9.
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Question : A boat goes 20 km upstream and 44 km downstream in 8 hours. In 5 hours, it goes 15 km upstream and 22 km downstream. Determine the speed of the boat in still water.
Option 1: 6 km/h
Option 2: 10 km/h
Option 3: 8 km/h
Option 4: 7 km/h
Question : A boat moves downstream at the rate of 1 km in $7\frac{1}{2}$ minutes and upstream at the rate of 5 km an hour. What is the speed of the boat in the still water?
Option 1: $3\frac{1}{2}$ km/hr
Option 2: $6\frac{1}{2}$ km/hr
Option 3: $4$ km/hr
Option 4: $8$ km/hr
Question : A boat moves downstream at a rate of 8 km/hr and upstream at 4 km/hr. The speed of the boat in still water is:
Option 1: 4.5 km/hr
Option 2: 5 km/hr
Option 3: 6 km/hr
Option 4: 6.4 km/hr
Question : A boat moves 25 km upstream and 39 km downstream in 8 hours. It travels 35 km upstream and 52 km downstream in 11 hours. What is the speed of the stream if it travels at a uniform speed?
Option 1: 4 km/hr
Option 4: 3 km/hr
Question : A boat covers 12 km upstream and 18 km downstream in 3 hours, while it covers 36 km upstream and 24 km downstream in $6\frac{1}{2}$ hours. What is the speed of the current?
Option 1: 1.5 km/hr
Option 2: 1 km/hr
Option 3: 2 km/hr
Option 4: 2.5 km/hr
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