Q1.
A person can swim downstream at 20 km/hr and can swim upstream at 18 km/hr . Find the person's speed in still water and the rate
of the stream ?
Solution.
Rate of person in still water =
1/2
(person's speed in downstream + person's
speed in upstream)
=
1/2
(20 + 18) =
1/2
(38) =
19 km/hr .
Rate of stream (current) =
1/2
(person's speed in downstream - person's
speed in upstream)
=
1/2
(20 - 18) =
1/2
(2) =
1 km/hr .
Solution
Q2.
A person swims downstream 33 km and upstream 21 km , taking 3 hrs in each case . find the velocity of person (in still water).
Person's dowhstream rate =
33/3
=
11 km/hr
Person's upstream rate =
21/3
= 7 km/hr
Velocity of person =
1/2
(11 + 7) = 9 km/hr
Q3.
A man can row upstream 54 km in 9 hrs and travel the same distance in 6 hrs . find the velocityof current .
Solution.
upstream rate =
54/9
= 6km/hr
downstream rate =
54/6
= 9 km/hr
Velocity of current =
1/2
(9 - 6) =
3/2
= 1.5 km/hr
Solution
Q4.
A person can sail 15 km/hr in still water . He takes twice as long as to row up as to row down the river . find the rate of stream .
Solution.
Assume person's rate with current = x km/hr
and person's rate against the current =
x/2
as per question
person's rate in still water =
1/2
(x +
x/2
)
3x/4
= 15 → x = 20
rate of stream is =
1/2
(20 - 10) = 5 km/hr
or
let the rate of stream = x km/hr
15 + x = 2(15 - x)
15 + x = 30 - 2x ⇒
- 15 = - 3x ⇒ x = 5 km/hr
Solution
Q5.
A man can row 10 km/h in still water . It takes thrice as long to row up as to row down the river . find the rate of the stream .
Solution.
Let rate of stream is x km/hr then as per question
(10 + x) = 3(10 - x)
10 + x = 30 - 3x
20 = 4x ⇒ x = 5 km/hr
Solution
Q6.
A man can swim 8 km/hr in still water . He takes twice as long to row up as to row down the river . find the rate of stream .
Solution.
Let rate of stream = x km/hr
then upstream rate = (8 - x)km/hr
downstream rate = (8 + x)km/hr
(8 + x) = 2(8 - x)
8 + x = 16 - 2x
8 = 3x ⇒ x = 8/3 km/hr
Solution
Q7.
A person can row 9 km/hr in still water . The speed of current is 3 km/hr , it takes him 2 hour to row to a particular place and
back . How far is the place .
Solution.
Let the required distance is x km
x/12
+
x/6
= 2
3x/12
= 2 ⇒ x = 8 km/hr
Solution
Q8.
A man can row 14 km/hr in still water. The speed of current is 2 km/hr , he takes 4 hrs to row to a place and back , How far is the place .
Solution.
Let t distance is x km
x/16
+
x/12
= 4
28x/16 x 12
= 4 ⇒
28x = 768
x = 27.4 km (Approx.)
or
Short Cut Trick d =
t(x2 - y2)/2x
d =
4(142 - 22)/2 x 14
= 27.4km(Approx.)
x = man's speed in still water , y = speed of current .
Solution
Q9.
Samir can row a certain distance downstream in 6 hours and return the same distance in 12 hours . If the current rate is 2 km/hr . find
speed of samir in still water .
Solution.
Let the speed of samir in still water is A
6(2 + A) = 12(A - 2)
12 + 6A = 12A - 24
- 6A = - 36
A = 6 km/hr
Short cut
=
CR(TD + TU)/( TU - TD)
=
2(6 + 12)/(12 - 6)
=
36/6
C
r =
Current rate
T
D = Downstream time , T
U = Upstream time .
Solution
Q10.
A person can row a certain distance downstream in 9 hours and return in 12 hours . Speed of current is 3 km/hr , find the speed of person
in still water and one side distance .
Solution.
Let speed of person in still water is m km/hr.
9(m + 3) = 12(m - 3)
9m + 27 = 12m - 36
-3m = - 63
m = 21 km/hr
distance = 24 x 9 = 216 km
Short cut
=
Cr(TD + TU)/( TU - TD)
=
3(12 + 9)/12 - 9
=
3 x 21/3
= 21 km/hr
distance = 24 x 9 = 216 km
Solution
