Home ≫ Arithmetic Aptitute ≫ Streams ≫ Page 2
11. A man can row 120 km downstream in 12 hours. If the speed of the current is 6 km/hr, then find in what time will he able to cover 32 km upstresam?
  A.  16 hours
  B.  12hours
  C.  15 hours
  D.  18 hours
     
   
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 =
32 / t
km/hr
Rate downstream =
120 / 12
= 10 km/hr
Here, upstream speed =
32 / t
, downstream speed = 10, a = 6
Using these values in the shortcut, we get:
6 =
1 / 2
(10 −
32 / t
)
6 x 2 = 10 −
32 / t

12 =
10t − 32 / t

12t = 10t − 32
12t − 10t = 32
2t = 32
t =
32 / 2
= 16
Hence, the man will take 16 hours.

12. A man can row three quarters of a km against the stream in 6
3 / 2
minutes and return in 3
3 / 4
minutes. Find the speed of the man in still water. What is the speed of the stream?
  A.  Man's speed in still water: 5 km/hr, Speed of stream: 2 km/hr
  B.  Man's speed in still water: 9 km/hr, Speed of stream: 3 km/hr
  C.  Man's speed in still water: 8 km/hr, Speed of stream: 3 km/hr
  D.  Man's speed in still water: 10 km/hr, Speed of stream: 5 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
60 / 15/2
=
3 / 4
x
60 x 2 / 15
= 6 km/hr
Rate downstream =
3 / 4
x
60 / 15/4
=
3 / 4
x
60 x 4 / 15
= 12 km/hr
Here, upstream speed = 6, downstream speed = 12, a = ?
Using these values in the shortcut, we get:
a =
1 / 2
(12 − 6)
a =
1 / 2
x 6 = 3
Hence, the rate of stream is 3km/hr.
Speed in still water =
1 / 2
(12 + 6)
=
1 / 2
x 18 = 9
Hence, the speed in still water is 9 km/hr.

13. A man takes twice as long to row up as to row down the river. If the rate of river is 8 km/hr, find the rate of the man in still water.
  A.  18 km/hr
  B.  15 km/hr
  C.  24 km/hr
  D.  21 km/hr
     
   
View Answer

Shortcut:
If a km/hr be the rate of the current, and a man takes m times as long to row up as to row down the river, then the rate of the man in still water is a
m + 1 / m − 1

Here, a = 8, m = 2
Required rate in still water = 8 x
2 + 1 / 2 − 1
= 8 x 3 = 24
Hence, the rate of man in still water is 24 km/hr.

14. A man can row 15 km/hr in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.
  A.  3 km/hr
  B.  6 km/hr
  C.  5 km/hr
  D.  8 km/hr
     
   
View Answer

Shortcut:
If a km/hr be the rate of the current, and a man takes m times as long to row up as to row down the river, then the rate of the man in still water is a x
m + 1 / m − 1

Here, a = 8, m = 2, Rate in still water = 15
Required rate in still water = a x
2 + 1 / 2 − 1

15 = 3a
a =
15 / 3
= 5
Hence, the rate of stream is 5 km/hr.

15. The speed of a boat in still water is 12 km/hr and the rate of current is 3 km/hr. Find the distance travelled downstream and upstream in 16 minutes.
  A.  Distance travelled downstream: 4 km; Distance travelled upstream:
12 / 5
km
  B.  Distance travelled downstream: 5 km; Distance travelled upstream:
13 / 7
km
  C.  Distance travelled downstream: 2 km; Distance travelled upstream:
10 / 3
km
  D.  Distance travelled downstream: 6 km; Distance travelled upstream:
11 / 6
km
     
   
View Answer

Shortcut:
If the speed of the boat in still water is a km/hr and the rate of current is b km/hr, then the distance travelled downstream in 't' hours is (a + b)t km the distance travelled upstream in 't' hours is (a − b)t km
Here, a = 12, b = 3, t = 16
Distance travelled downstream = (a + b)t = (12 + 3)16 = 15 x
16 / 60
= 4 km/hr
Distance travelled upstream = (a − b)t = (12 − 3)
16 / 60
= 9 x
16 / 60
=
3 x 4 / 5
=
12 / 5
km/hr

16. The speed of a boat in still water is 14 km/hr and the rate of current is 2 km/hr. The distance travelled downstream in 15 minutes is:
  A.  5 km
  B.  7 km
  C.  2 km
  D.  4 km
     
   
View Answer

Shortcut:
If the speed of the boat in still water is a km/hr and the rate of current is b km/hr, then the distance travelled downstream in 't' hours is (a + b)t km the distance travelled upstream in 't' hours is (a − b)t km
Here, a = 14, b = 2, t = 15
Distance travelled downstream = (a + b)t = (14 + 2)
15 / 60
= 16 x
15 / 60
= 4 km/hr

17. Speed of a boat in standing water is 14 km/hr and the speed of the stream is 3 km/hr. A distance of 55 km, going upstream is covered in.
  A.  5 hour
  B.  8 hour
  C.  6 hour
  D.  2 hour
     
   
View Answer

Shortcut:
If the speed of the boat in still water is a km/hr and the rate of current is b km/hr, then the distance travelled downstream in 't' hours is (a + b)t km the distance travelled upstream in 't' hours is (a − b)t km
Upstream rate =
36 / 6
= 6 km/hr
Speed of man in still water = 6 + 3 = 9 km/hr
Here, a = 14, b = 3, t = ?, Distance = 55
Distance travelled downstream = (a − b)t
55 = (14 − 3) x t
55 = 11 x t
t =
55 / 11
= 5 hour

18. A man can row upstream 36 km in 6 hours. If the speed of current is 3 km/hr, find how much he can go downstream in 5 hours.
  A.  60 km
  B.  50 km
  C.  65 km
  D.  55 km
     
   
View Answer

Shortcut:
If the speed of the boat in still water is a km/hr and the rate of current is b km/hr, then the distance travelled downstream in 't' hours is (a + b)t km the distance travelled upstream in 't' hours is (a − b)t km
Upstream rate =
36 / 6
= 6 km/hr
Speed of man in still water = 6 + 3 = 9 km/hr
Here, a = 9, b = 3, t = 5
Distance travelled downstream = (a + b)t = (9 + 3) x 5 = 12 x 5 = 60 km

19. A man can row upstream 24 km in 4 hours. If the speed of a man in still water is 10 km/hr, find how much he can go downstream in 8 hours.
  A.  115 km
  B.  112 km
  C.  110 km
  D.  120 km
     
   
View Answer

Shortcut:
If the speed of the boat in still water is a km/hr and the rate of current is b km/hr, then the distance travelled downstream in 't' hours is (a + b)t km the distance travelled upstream in 't' hours is (a − b)t km
Speed of current = 10 −
24 / 4
= 10 − 6 = 4 km/hr
Here, a = 10, b = 4, t = 8
Distance travelled downstream = (a + b)t = (10 + 4) x 8 = 14 x 8 = 112 km

20. The speed of a boat in still water is 6 km/hr and the speed of current is 4 km/hr. If the time taken to reach a certain distance upstream is 5 hours, find the time it will take to go to same distance downstream.
  A.  2 hour
  B.  3 hour
  C.  4 hour
  D.  1 hour
     
   
View Answer

Shortcut:
If the speed of the boat in still water is a km/hr and the rate of current is b km/hr, then the distance travelled downstream in 't' hours is (a + b)t km the distance travelled upstream in 't' hours is (a − b)t km
Here, a = 6, b = 4, t = 5
Distance travelled upstream = (a − b)t = (6 − 4) x 5 = 2 x 5 = 10 km
∴ Required time =
10 / 6 + 4
=
10 / 10
= 1 hour.

Copyright © 2020-2022. All rights reserved. Designed, Developed and content provided by Anjula Graphics & Web Desigining .