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31. Ram can row a certain distance downstream in 6 hours and return the same distance in 9 hours. If the stream flows at the rate of 3 km/hr find the speed of Ram in still water.
  A.  11 km/hr
  B.  15 km/hr
  C.  20 km/hr
  D.  13 km/hr
     
   
View Answer

Shortcut:
A man rows a certain distance downstream in h1 hours and returns the same distance in h2 hours. If the stream flows at the rate of a km/hr then the speed of the man in still water is
a(h1 + h2) / h2 − h1
km/hr
Here, h1 = 6, h2 = 9, a = 3
Speed in still water =
3(6 + 9) / 9 − 6

=
3 x 15 / 3
= 15
Hence, the speed in still water is 15 km/hr.

32. Ram can row a certain distance downstream in 6 hours and return the same distance in 9 hours. If the speed of Ram in still water is 12 km/hr, find the speed of the stream.
  A.  3.6 km/hr
  B.  4.2 km/hr
  C.  2.4 km/hr
  D.  1.8 km/hr
     
   
View Answer

Shortcut:
A man rows a certain distance downstream in h1 hours and returns the same distance in h2 hours. If the stream flows at the rate of a km/hr then the speed of the man in still water is
a(h1 + h2) / h2 − h1
km/hr
Here, h1 = 6, h2 = 9, a = ?, Speed in still water = 12
Speed in still water =
a(6 + 9) / 9 − 6

12 =
a x 15 / 3

12 x 3 = a x 15
a =
12 x 3 / 15
=
12 / 5
= 2.4
Hence, the speed of the stream is 2.4 km/hr.

33. A man can row at a speed of 5 km/hr in still water to a certain upstream point and back to the starting point in a river which flows at 2 km/hr. Find his avertage speed for total journey.
  A.  3
1 / 5
km/hr
  B.  5
1 / 4
km/hr
  C.  6
2 / 5
km/hr
  D.  4
1 / 5
km/hr
     
   
View Answer

Shortcut:
If a man can row at a speed of a km/hr in still water to a certain upstream point and back to the starting point in a river which flows at b km/hr, then the average speed for total journey is
(a + b)(a − b) / a
km/hr
Here, a = 5, b = 2
Average Speed =
(5 + 2)(5 − 2) / 5

=
7 x 3 / 5
=
21 / 5
= 4
1 / 5

Hence, his averge speed for total journey is 4
1 / 5
km/hr.

34. A man can row 6 km/hr in still water. If the river is running at 2 km/hr, it takes 3 hours more in upstream than to go downstream for the same distance. How far is the place?
  A.  24 km
  B.  18 km
  C.  25 km
  D.  22 km
     
   
View Answer

Shortcut:
A man can row a km/hr in still water. If the stream is flowing at b km/hr, it takes him D hours more in upstream than to go downstream for the same distance, then the distance is
D(a2 − b2) / 2b
km
Here, D = 3, a = 6, b = 2
Required distance =
3 x [(6)2 − (2)2] / 2 x 2

=
3 x (36 − 4) / 4
=
3 x 32 / 4
= 3 x 8 = 24
Hence, total distance is 24 km.

35. A man can row 45 km upstream and 66 km downstream in 15 hours. Also, he can row 60 km upstream and 82.5 km downstream in 19
1 / 2
hours. Find the rate of the current and the speed of the man in still water.
  A.  6 km/hr, 4 km/hr
  B.  7 km/hr, 3 km/hr
  C.  8 km/hr, 3 km/hr
  D.  3 km/hr, 2 km/hr
     
   
View Answer

Shortcut:
A man can row a1 km upstream and b1 km downstream in t1 hours. Also, he can row a2 km upstream and b2 km downstream in t2 hours. Then, the rate of the currrent and speed of the man in still water is calculated by the use of multiple cross-multiplication method as in 2 steps:

Step 1 :Arrange the given figures in the following form

Upstream Downstream Time
a1 b1 t1
a2 b2 t2
Upstream speed of man =
a1b2 − a2b1 / b2t1 − b1t2
km/hr
Downstream speed of man =
a1b2 − a2b1 / a1t2 − a2t1
km/hr
Step 2: To calculate the speed of man and current, use the following formula.

Speed of man =
1 / 2
(upstream speed of man + downstream speed of man)
Speed of stream =
1 / 2
(downstream speed of man − upstream speed of man)

Here, a1 = 45, a2 = 60, b1 = 66, b2 = 82.5, t1 = 15, t2 = 19
1 / 2
or
39 / 2


Upstream Downstream Time
45 66 15
60 82.5 39/2

Upstream speed of man =
45 x 82.5 − 60 x 66 / 82.5 x 15 − 66 x 39/2

=
3712.5 − 3960 / 1237.5 − 1287
=
− 247.5 / − 49.5
= 5
Hence, the upstream speed of man is 5 km/hr.
Downstream speed of man =
45 x 82.5 − 60 x 66 / 45 x 39/2 − 60 x 15

=
3712.5 − 3960 / 877.5 − 900
=
− 247.5 / − 22.5
= 11
Hence, the downstream speed of man is 11 km/hr.
Speed of man =
1 / 2
(5 + 11) =
16 / 2
= 8
Hence, the speed of man is 8 km/hr.
Speed of stream =
1 / 2
(11 − 5) =
6 / 2
= 3
Hence, the speed of stream is 3 km/hr.

36. A can row a certain distance downstream in 6 hours and return the same distance in 9 hours. if the stream flows at the rate of 2
1 / 4
km/hr, find his speed in still water?
  A.  9
3 / 4
km/hr
  B.  11
1 / 4
km/hr
  C.  13
4 / 5
km/hr
  D.  10
7 / 4
km/hr
     
   
View Answer

Shortcut:
A man rows a certain distance downstream in h1 hours and returns the same distance in h2 hours. If the stream flows at the rate of a km/hr then the speed of the man in still water is
a(h1 + h2) / h2 − h1
km/hr
Here, h1 = 6, h2 = 9, a = 9/4
Speed in still water =
9/4(6 + 9) / 9 − 6

=
9/4 x 15 / 3
=
9 x 5 / 4
=
45 / 4
= 11
1 / 4

Hence, the speed in still water is 11
1 / 4
km/hr.

37. A man can row at a speed of 4.5 km/hr in still water to a certain upstream point and back to the starting point in a river which flows at 1.5 km/hr. Find his average speed of total journey.
  A.  3 km/hr
  B.  2 km/hr
  C.  5 km/hr
  D.  4 km/hr
     
   
View Answer

Shortcut:
If a man can row at a speed of a km/hr in still water to a certain upstream point and back to the starting point in a river which flows at b km/hr, then the average speed for total journey is
(a + b)(a − b) / a
km/hr
Here, a = 4.5, b = 1.5
Average Speed =
(4.5 + 1.5)(4.5 − 1.5) / 4.5

=
6 x 3 / 4.5
=
6 x 3 x 10 / 45
= 2 x 2 = 4
Hence, his averge speed for total journey is 4 km/hr.

38. A boat takes 3 hours to travel from place M to N downstream and back from N to M upstream. If the speed of the boat in still water is 4 km, what is the distance between the two places?
  A.  3 km
  B.  1 km
  C.  Data inadequate
  D.  4 km
     
   
View Answer

Let the distance between M and N and the speed of current in still water be a km and b km/hr respectively.
As per question:
a / 4 + b
+
a / 4 − b
= 3
In the above equation we have only one equation having two variables. Hence can't be determined.

39. A man rows to a place 48 km distance and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. Find the rate of the stream?
  A.  1 km/hr
  B.  4 km/hr
  C.  3 km/hr
  D.  2 km/hr
     
   
View Answer

Let the man takes a hours to cover 4 km downstream anda hours to cover 3 km upstream.
Then,
48a / 4
+
48a / 3
= 14
3 x 48a + 4 x 48a / 12
= 14
144a + 192a = 14 x 12
336a = 168
a =
168 / 336
=
1 / 2

∴ Rate upstream = 6 km/hr and rate downstream = 8 km/hr
∴ Rate of the stream =
1 / 2
(8 − 6) =
1 / 2
x 2 = 1
Hence, the rate of stream is 1 km/hr.

40. A, B and C are the three towns on a river which flows uniformly. B is equidistant from A and C. Ram rows from A to B and back in 10 hours and he can row from A to C in 4 hours. Compare the speed of his boat in still water with that of the river.
  A.  3 : 2
  B.  5 : 3
  C.  2 : 5
  D.  3 : 5
     
   
View Answer

Ram can row from A to C in 4 hours
∴ He can row from A to B in 2 hours.
But he can row rom A to B an back in 10 hours.
∴ he can row from B to A in ( 10 − 2) = 8 hours.
Hence in rowing with the current he take 2 hours and in rowing against the current he takes 8 hours, the distance being same in both the cases.
Now, distance being the same the downrate and the uprate are inversely proportional to the times.
∴ downrate : up rate = 8 : 2 = 4 : 1
∴ speed of boat in still water : speed of river = 4 + 1 : 4 − 1 = 5 : 3

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