Question : A man rows from J to K (upstream) and back from K to J (downstream) in a total time of 15 hours. The distance between J and K is 300 km. The time taken by the man to row 9 km downstream is identical to the time taken by him to row 3 km upstream. What is the approximate speed of the boat in still water?
Option 1: 51.33 km/hr
Option 2: 47.67 km/hr
Option 3: 53.33 km/hr
Option 4: 43.67 km/hr
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Correct Answer: 53.33 km/hr
Solution : Let the speed of the boat as B and the speed of the stream as S. Upstream Speed = B – S Downstream Speed = B + S ⇒ A man rows from J to K (upstream) and back from K to J(downstream) in a total time of 15 hours. The distance between J and K is 300 km. According to the question, $\frac{300}{B + S}$ + $\frac{300}{B – S}$ = 15 ⇒ $\frac{20}{B + S}$ + $\frac{20}{B – S}$ = 1 Since the time taken by him to row 3 km upstream is equal to the time taken by him to row 9 km downstream. So, $\frac{9}{B + S}$ = $\frac{3}{B – S}$ ⇒ $\frac{B + S}{B - S}$ = $\frac{3}{1}$ From this, we can take the speed of the boat as B = 2$x$ km/hr, and the speed of the stream as S = $x$ km/hr So, $\frac{20}{ 2x + x} + \frac{20}{2x – x}=1$ ⇒ $\frac{20}{ 3x } + \frac{20}{x}=1$ ⇒ $x = \frac{80}{3}$ So, the speed of boat in still water, B = 2$x$ km/hr = 2 × $\frac{80}{3}$ = 53.33 km/hr Hence, the correct answer is 53.33 km/hr.
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Question : A man rows from A to B (upstream) and B to A (downstream) in 12 hours. The distance between A and B is 240 km. The time taken by the man to row 6 km downstream is identical to the time taken by him to row 4 km upstream. What is the speed of the stream?
Option 1: $\frac{35}{3}$ km/hr
Option 2: $\frac{25}{3}$ km/hr
Option 3: $\frac{46}{3}$ km/hr
Option 4: $\frac{50}{3}$ km/hr
Question : The speed of a boat upstream is 8 km/hr and the speed of a stream is 4 km/hr. The boat covers a distance of $x$ km in upstream and $x$ km in downstream. If the total time taken by the boat is 9 hours, then what is the value of $x$?
Option 1: 60 km
Option 2: 72 km
Option 3: 48 km
Option 4: 36 km
Question : The time taken by boat to cover a distance of x km in upstream is 3 hours more than the time taken by the boat to cover the same distance in downstream. The speed of the boat in upstream is 8 km/hr. Which of the following statement(s) is/are correct? I. If the value of x is 48 km, then the speed of the boat in downstream is 16 km/hr. II. If the speed of the boat in downstream is 12 km/hr, then the value of x is 48 km.
Option 1: Neither I nor II
Option 2: Only II
Option 3: Only I
Option 4: Both I and II
Question : A boat can row 24 km in 6 hours in still water It can row 56 km downstream and 30 km upstream in 38 hours. What is the speed of the stream?
Option 1: 3 km/hr
Option 2: 5 km/hr
Option 3: 3.5 km/hr
Option 4: 4 km/hr
Question : A boat can travel at a speed of 15 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 80 km downstream.
Option 1: 3 hr
Option 2: 4 hr
Option 3: 6 hr
Option 4: 5 hr
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