1. A boat goes 20 km upstream in 2 hours and downstream in 1 hour. How much time this boat will take to travel 30 km in all still water?
A. 1 hr
B. 2 hrs
C. 1.5 hrs
D. 2.5 hrs
Answer - Option B
Explanation -
Let [latex] {v}_{1}[/latex] be the speed of boat in still water and [latex] {v}_{2}[/latex] be the speed of current
[latex] {v}_{1} + {v}_{2}[/latex] = [latex]\frac {20}{1}[/latex] = 20 ......(1)
[latex]{v}_{1} - {v}_{2}[/latex] = [latex]\frac {20}{2}[/latex] = 10 ......(2)
From equations (i) and (ii) we get
[latex]{v}_{1}[/latex] = 15 km/hr
[latex]\frac {d}{{v}_{1}} [/latex] = [latex]\frac {30}{15}[/latex] = 2 hrs
2. In the above question, the speed at which the stream is flowing is
A. 10 km/hr
B. 20 km/hr
C. 15 km/hr
D. 5 km/hr
Answer - Option D
Explanation -
From the above two equation, we get [latex]\frac {d}{{v}_{2}} [/latex] = 5 km/hr
3. A boat travels 10 km in 1 hr downstream and 14 km in 2 hrs upstream. How much time this boat will take to travel 17 km in still water?
A. 1 hr
B. 2 [latex]\frac {1} {2}[/latex]hrs
C. 2 hrs
D. 2 [latex]\frac {1} {2}[/latex]hrs
Answer - Option C
Explanation -
[latex] {v}_{1} + {v}_{2}[/latex] = [latex]\frac {10}{1}[/latex] = 10 ......(1)
[latex] {v}_{1} - {v}_{2}[/latex] = [latex]\frac {14}{2}[/latex] = 7 ......(2)
Adding equations (i) and (ii), we get
[latex]{v}_{1}[/latex] = [latex]\frac {17}{2}[/latex] km/hr
[latex]\frac {d}{{v}_{1}} [/latex] = [latex]\frac {17}{\frac{17}{2}}[/latex] = 2 hrs
4. A man goes by motor boat a certain distance up stream at 15 km/hr and return the same
downstream at 20 km/hr. The total time taken for the journey was 7 hrs. Find how far did he go.
A. 60 km
B. 50 km
C. 40 km
D. 120 km
Answer - Option A
Explanation -
[latex]\frac {d}{20} + \frac {d}{10}[/latex] = 7
d = 60 km
5. A man can row upstream a distance of [latex]\frac {2} {3}[/latex] km in 10 minutes and returns the same distance downstream in 5 minutes. Ratio of man’s speed in still water and that of the stream will be
A. 3 : 1
B. 1: 3
C. 2 : 3
D. 3 : 2
Answer - Option A
Explanation -
[latex] {v}_{1} - {v}_{2}[/latex] = [latex]\frac {\frac{2}{3}km}{10 min}[/latex]
i.e, [latex] {v}_{1} - {v}_{2}[/latex] = [latex]\frac {2}{30}[/latex] km/min ......(1)
and [latex] {v}_{1} + {v}_{2}[/latex] = [latex]\frac {\frac{2}{3} km}{5 min}[/latex] = 10
[latex] {v}_{1} + {v}_{2}[/latex] = [latex]\frac {2}{15}[/latex] = 7 ......(2)
Solving equation (i) and (ii), we get
[latex] {v}_{1}[/latex] = [latex]\frac {2 + 4}{60}[/latex] km/min = [latex]\frac {6}{60}[/latex] km/min = [latex]\frac {1}{10}[/latex] km/min
[latex] {v}_{2}[/latex] = [latex]\frac {4 - 2}{60}[/latex] km/min = [latex]\frac {2}{60}[/latex] km/min = [latex]\frac {1}{30}[/latex] km/min
[latex] \frac{{v}_{1}}{{V}_{2}}[/latex] = [latex]\frac {1}{10}[/latex] * [latex]\frac {30}{1}[/latex] = 3 : 1