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1. Speed of a man is 8 km/hr in still water. If the rate of current is 3 km/hr, find the effective speed of the man upstream.
  A.  11 km/hr
  B.  3 km/hr
  C.  5 km/hr
  D.  2 km/hr
     
   
View Answer

Shortcut:
If the speed of the boat ( or the swimmer) is a km/hr and if the speed of the stream is b km/hr then, while upstream the effective speed of the boat is (a − b) km/hr
Here, a = 8, b = 3
∴ Effective speed of the man upstream = (8 − 3) = 5km/hr

2. The speed of a boat in still water is 2 km/hr. If its speed upstream be 1 km/hr, then speed of the stream is:
  A.  1 km/hr
  B.  2 km/hr
  C.  3 km/hr
  D.  4 km/hr
     
   
View Answer

Shortcut:
If the speed of the boat ( or the swimmer) is a km/hr and if the speed of the stream is b km/hr then, while upstream the effective speed of the boat is (a − b) km/hr
Here, a = 2, b = ?
∴ Effective speed of the upstream = (2 − b)
1 = (2 − b)
b = 2 − 1 = 1 km/hr

3. Speed of a swimmer is 8 km/hr in still water. If the rate of stream is 3 km/hr, find the effective speed of the swimmer downstream.
  A.  10 km/hr
  B.  12 km/hr
  C.  11 km/hr
  D.  None of the above
     
   
View Answer

Shortcut:
If the speed of the boat ( or the swimmer) is a km/hr and if the speed of the stream is b km/hr then, while downstream the effective speed of the boat is (a + b) km/hr
Here, a = 8, b = 3
∴ Effective speed of the man upstream = (8 + 3) = 11 km/hr

4. A boat goes 12 km upstream in 48 minutes. The speed of stream is 2 km/hr. The speed of boat in still water is:
  A.  14 km/hr
  B.  25 km/hr
  C.  17 km/hr
  D.  20 km/hr
     
   
View Answer

Shortcut:
If the speed of the boat ( or the swimmer) is a km/hr and if the speed of the stream is b km/hr then, while downstream the effective speed of the boat is (a + b) km/hr
Upstream speed = Distance/time =
12 / 48/60
=
60 / 4
= 15 km/hr Here, a = 15, b = 2
∴ Effective speed of the man upstream = (15 + 2) = 17 km/hr

5. A man can row upstream at 10 km/hr and downstream at 16 km/hr. Find the man's rate in still water.
  A.  11 km/hr
  B.  20 km/hr
  C.  15 km/hr
  D.  13 km/hr
     
   
View Answer

Shortcut:
If a km/hr be the man's rate in still water, then a =
1 / 2
(man's rate with current + his rate against current)
Here, upstream speed = 10, downstream speed = 16
Using these values in the shortcut, we get:
Man's speed in still water =
1 / 2
(16 + 10)
=
1 / 2
x 26 = 13 km/hr

6. A man can row 44 km downstream in 4 hours. If the man's rowing rate in still water is 8 km/hr, then find in what time will he cover 25 km upstream?
  A.  10 hours
  B.  5 hours
  C.  7 hours
  D.  4 hours
     
   
View Answer

Shortcut:
If a km/hr be the man's rate in still water, then a =
1 / 2
(man's rate with current + his rate against current)
Downstream speed =
44 / 4
= 11 km/hr
Here, a = 8, upstream speed = z, downstream speed = 11
Using these values in the shortcut, we get:
8 =
1 / 2
(11 + z)
8 x 2 = 11 + z
16 = 11 + z
z = 16 − 11 = 5 km/hr
Hence, upstream speed = 5 km/hr
⇒ 5 km in 1 hour
Hence, 25 km will be covered in 5 hour.

7. If a man's downstream rate is 10 km/hr, and the rate of stream is 1.5 km/hr, then the man's upstream rate is
  A.  7 km/hr
  B.  9 km/hr
  C.  5 km/hr
  D.  11 km/hr
     
   
View Answer

Shortcut:
If a km/hr be the rate of stream, then a =
1 / 2
(downstream rate − upstream rate)
Here, a = 1.5, upstream speed = z, downstream speed = 10
Using these values in the shortcut, we get:
1.5 =
1 / 2
(10 − z)
1.5 x 2 = 10 − z
3 = 10 − z
z = 10 − 3 = 7
Hence, upstream speed = 7 km/hr

8. If a man rows at 8 km/hr in still water and his upstream rate is 5 km/hr, then the man's rate along the current (downstream) is:
  A.  15 km/hr
  B.  10 km/hr
  C.  12 km/hr
  D.  11 km/hr
     
   
View Answer

Shortcut:
If a km/hr be the man's rate in still water, then a =
1 / 2
(man's rate with current + his rate against current)
Downstream speed =
44 / 4
= 11 km/hr
Here, a = 8, upstream speed = z, downstream speed = 5
Using these values in the shortcut, we get:
8 =
1 / 2
(5 + z)
8 x 2 = 5 + z
16 = 5 + z
z = 16 − 5 = 11 km/hr
Hence, upstream speed = 11 km/hr

9. A man can row upstream at 10 km/hr and downstream at 16 km/hr. Find the rate of the current.
  A.  4 km/hr
  B.  5 km/hr
  C.  3 km/hr
  D.  2 km/hr
     
   
View Answer

Shortcut:
If a km/hr be the rate of the current, then a =
1 / 2
(man's rate with current − his rate against current)
Here, upstream speed = 10, downstream speed = 16
Using these values in the shortcut, we get:
a =
1 / 2
(16 − 10)
a =
1 / 2
x 6
a = 3
Hence, rate of current = 3 km/hr

10. A man can row three quarters of a km against the stream in 11 minutes 15 seconds and return in 7 minutes 30 seconds. Find the speed of the man in still water and also the speed of the stream
  A.  Speed of man in still water: 4 km/hr; Speed of the stream: 2 km/hr
  B.  Speed of man in still water: 5 km/hr; Speed of the stream: 1 km/hr
  C.  Speed of man in still water: 7 km/hr; Speed of the stream: 1 km/hr
  D.  Speed of man in still water: 5 km/hr; Speed of the stream: 2 km/hr
     
   
View Answer

Shortcut:
If a km/hr be the rate of the current, then a =
1 / 2
(man's rate with current − his rate against current)
Rate upstream =
3 / 4
x
4 / 45
x 60 = 4 km/hr
Rate downstream =
3 / 4
x
2 / 15
x 60 = 6 km/hr
Here, upstream speed = 4, downstream speed = 6
Using these values in the shortcut, we get:
a =
1 / 2
(6 − 4)
a =
1 / 2
x 2
a = 1
Hence, rate of current = 1 km/hr
Speed in still water =
1 / 2
(6 + 4) =
1 / 2
x 10 = 5
Hence, speed in still water is 5 km/hr.

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