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

1. A man can row a certain distance down stream in 6 hours and return the same distance in 9 hours. If stream flows at the rate of 2 km/hr, then what will be man’s speed if he rows in still water?

A. 10 km/hr B. 12 km/hr C. 14 km/hr D. 15 km/hr

Answer - Option A
Explanation -
[latex]( {v}_{1} + {v}_{2}) {t}_{1}[/latex] = [latex]( {v}_{1} - {v}_{2}) {t}_{2}[/latex]
i.e, [latex]( {v}_{1} + {v}_{2}) * 6[/latex] = [latex]( {v}_{1} - {v}_{2}) * 9[/latex]
[latex]( {v}_{1}[/latex] = 10 km/hr
2. A boat against the current of water goes 9 km/hr and in the direction of the current 12 km/hr. The boat takes 4 hours and 12 minute es to move upward and downward direction from A to B. What is the distance between A and B?

A. 21.6 km B. 21.0 km C. 22 km D. 30 km

Answer - Option A
Explanation -
[latex]\frac {d}{9} + \frac {d}{12}[/latex] = [latex]4 \frac {12}{60}[/latex]
d = 21.6 km
3. A man takes 3 hours and 45 minutes to boat 15 km with the current in a river and 2 hours 30 minutes to cover a distance of 5 km against the current. Speed of the boat in still water and speed of the current respectively will be

A. 3 km/hr, 1 km/hr B. 1 km/hr, 3 km/hr C. 2 km/hr, 5 km/hr D. none of these

Answer - Option A
Explanation -
[latex]({v}_{1} + {v}_{2})[/latex] = [latex] \frac {15}{3 \frac {3}{4}}[/latex] = 4 km/hr
[latex] ({v}_{1} - {v}_{2})[/latex] = [latex] \frac {5}{2 \frac {1}{2}}[/latex] = 2 km/hr
Solving equations (i) and (ii), we get
[latex] {v}_{1}[/latex] = 3 km/hr and [latex]{v}_{2}[/latex] = 1 km/hr
4. A boat can be rowed 6 km/hr along the current and 4 km/hr against the current. Speed of the current and speed of the boat in still water, respectively will be

A. 1 km/hr, 5 km/hr B. 5 km/hr, 1 km/hr C. 2 km/hr, 4 km/hr D. none of these

Answer - Option B
Explanation -
[latex]({v}_{1} + {v}_{2})[/latex] = 6 .....(1)
[latex]( {v}_{1} - {v}_{2})[/latex] = 4 .....(2)
From equations (i) and (ii), we get
[latex] {v}_{1}[/latex] = 5 km/hr and [latex]{v}_{2}[/latex] = 1 km/hr
5. A boat moves down the stream at the rate of 1 km in 6 minutes and up the stream at the rate of 1 km in 10 minutes. The speed of the current is

A. 2 km/hr B. 1 km/hr C. 1.5 km/hr D. 2.5 km/hr

Answer - Option A
Explanation -
[latex]({v}_{1} + {v}_{2})[/latex] = [latex] \frac {1 km}{6 min}[/latex] = 10 km/hr ...(1)
[latex]({v}_{1} - {v}_{2})[/latex] = [latex] \frac {1 km}{10 min}[/latex] = 6 km/hr ....(2)
subtracting equation (2) from (1), we get
[latex]{v}_{1}[/latex] = 2 km/hr

1. A man can row 5 km per hour in still water. If the river is flowing at 1km per hour, it takes him 75 minutes to row to a place and back. How far is the place?

A. 3 km B. 2.5 km C. 4 km D. None of these

Answer - Option A
Explanation -
[latex]\frac {d}{5 + 1} + \frac {d}{5 - 1}[/latex] = [latex]\frac {75}{60}[/latex]
[latex]\frac {2d + 3d}{12}[/latex] = [latex]\frac {5}{4}[/latex]
d = 3 km
2. Speed of a boat in still water is 7 km/hr and speed of the stream is 1.5 km/hr . How much time will it take to move up is stream of a distance 7.7 km?

A. 75 minutes B. 84 minutes C. 72 minutes D. None of these

Answer - Option B
Explanation -
t = [latex]\frac {d}{{v}_{1} + {v}_{2}}[/latex] = [latex]\frac {7.7}{7 + 1.5}[/latex] = [latex]\frac {7.7}{5.5}[/latex]
= [latex]\frac {7}{5}[/latex] hrs = [latex]\frac {7}{5} * 60 min[/latex] = 84 min
3. A motorboat takes 2 hours to travel a distance of 9 km down the current and it takes 6 hours to travel the same distance against the current. What is the speed of the boat in still water in kmph?

A. 3 B. 2 C. 1.5 D. 1

Answer - Option A
Explanation -
Let the speed of boat in still water and speed of current are x and y km/h respectively.
i.e, Downward speed of boat = (x + y) km/h.
According to question,
x + y = [latex]\frac {9}{2}[/latex]
2x + 2y = 9 ...(i)
x - y = [latex]\frac {9}{6}[/latex]
2x – 2y = 3 ...(ii)
On solving equations (i) and (ii), we get
x = 3, y = [latex]\frac {3}{2}[/latex]