 Important for :
1
Amit goes Mumbai to Kolkata by sea route. The speed of the boat in still water is 60 km/h and speed of the current is 15 km/h. After reaching Kolkata he stayed there for 20 minutes and after that come back by same boat. The time taken by him in this journey is 19 hours 32 minutes, find the distance travel by him in one side.
» Explain it
C

Time taken by him in travelling = 19 hours 32 minutes – 20 minutes
= 19 hours 12 minutes

Let Distance = x km

According to the question,

 x + x = 19 12 60+15 60 – 15 60

 x + x = 96 75 45 5

 5x + 3x = 96 225 5

 8x = 96 225 5

x = 540 km

Hence, option C is correct.

2
A man can row at a speed of 12 km/hr in still water to a certain upstream point and back to the starting point in a river which flows at 3 km/hr. Find his average speed for total journey.
» Explain it
D
Speed of the man in still water = 12 km/hr

Speed of the stream = 3 km/hr

Speed downstream = (12 + 3) = 15 km/hr

Speed upstream = (12 – 3) = 9 km/hr

Let the distance travelled be ‘d’ km Then

 Average Speed = total distance total time

 = d + d d + d 15 9

 = 2d 9d + 15 d 15 × 9

 = 2d × (15 × 9) = 45 km/hr = 11 1 km/hr 24d 4 4

Hence, option (D) is correct.
3
The ratio of the speed of boat in still water to the speed of stream is 16 : 5. A boat goes 16.5 km in 45 minute upstream, find the time taken by boat to cover the distance of 17.5 km downstream.
» Explain it
B
Let the speed of boat in still water = 16x, speed of stream = 5x

Upstream speed = 16x – 5x = 11x

 S = D t

 11x = 16.5 × 60 45

x = 2

speed of boat in still water = 32 km/h, speed of stream = 10 km/h

Downstream speed = 32 + 10 = 42 km/h

Distance = 17.5 km

 time = 17.5 42

 = 5 hour 12

 or 5 × 60 = 25 minutes 12

Hence, option B is correct.

4
If the ratio of speed of boat in downstream and speed of stream is 9 : 1, speed of current is 3 km per hr, What would be the distance travelled in upstream by the boat in 5 hours?
» Explain it
D
Ratio of speed of boat in downstream and speed of stream is 9 : 1

Given Speed of current = 3 km/ h

Speed of boat in downstream = 9 × 3 = 27 km/h

Speed of boat in still water = Speed of boat in downstream – Speed of current

= 27 – 3 = 24 km/h

Speed of boat in upstream = 24 – 3 = 21 km/h

Distance travelled by boat in upstream in 5 hours = 21 × 5 = 105 km

Hence, option D is correct.

5
In a river, the ratio of the speed of the stream and the speed of a boat in still water is 5 : 7. Again, the ratio of the speed of the stream to the speed of another boat in still water is 6 : 8. What is the ratio of the speed of the first boat to that of the second boat in still water?
» Explain it
B
For the first boat let the speed of the stream be 5x and the speed of the boat be 7x.

For the 2nd boat, let the speed of the stream be 6y and the speed of the 2nd boat be 8y.

The speed of the stream will be the same.

5x = 6y

 or, x = 6 y 5

Now, the required ratio of the speed of the first boat to that of the second boat = 7x : 8y

 ⇒  7 × 6 y : 8y 5

[Putting x in terms of y]

 ∴ 21 y : 4y = 21 : 20 5

Hence, option B is correct.