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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