Question : A boat can go 5 km upstream and $7 \frac{1}{2}$ km downstream in 45 minutes. It can also go 5 km downstream and 2.5 km upstream in 25 minutes. How much time (in minutes) will it take to go 6 km upstream?
Option 1: 30
Option 2: 36
Option 3: 24
Option 4: 32
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Correct Answer: 36
Solution : Given, A boat can go 5 km upstream and 7$\frac{1}2{}$ downstream in 45 minutes. It can go 5 km downstream and 2.5 km upstream in 25 minutes. We know, Time = $\frac{\text{Distance}}{\text{Speed}}$ Let the speed of the boat upstream be U and the speed of the boat downstream be D A boat can go 5 km upstream and 7$\frac{1}2{}$ km downstream in 45 minutes ⇒ Time = 45 × $\frac{1}{60}$ hr ⇒ Time = $\frac{3}{4}$ hrs Now, $\frac{5}{U} + \frac{15}{2D} = \frac{3}{4}$ ⇒ $\frac{15 U + 10 D}{2DU} = \frac{3}{4}$ ⇒ $60U + 40D = 6DU$...........(1) It can go 5 km downstream and 2.5 km upstream in 25 minutes. ⇒ Time = $\frac{25}{60}$ hr ⇒ Time = $\frac{5}{12}$ hrs ⇒ $\frac{5}{D} + \frac{2.5}{U} = \frac{5}{12}$ ⇒ $60U + 30D = 5DU$...............(2) By solving equations (1) and (2) we get U = 10 km/hr Now, the Time taken to cover 6 km upstream, = $\frac{6}{10}$ = 0.6 hr = 36 minutes Hence, the correct answer is 36.
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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?
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?
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?
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.
Question : A boat can cover 120 km upstream and back in a total of 30 hours, and 25 km upstream and 40 km downstream in a total of 7 hours. How much distance will the boat cover in 16 hours in still water?
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