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Answers :-
1. (b) Let the speed of boat in still water = x km/h
Speed of stream = y km/h
Speed of boat in the downstream, D = (x + y) km/h
Speed of boat in the upstream, U
= (x – y) km/h
distance to be covered = 18 km
D = x + y = 18 km/4h = 9/2 km/h ………….. (i)
U = x – y = 18km/ 12h = 3/2 km/h ………. (ii)
On solving (i) and (ii)
y =[(9/2 – 3/2) /2] = 1.5 km/hr.
Alternate:
Speed of stream = ½ (D – U)
Speed of boat = ½ (D + U)
Now, By using those above Formula’s
Speed of Stream
= (1/2) (9/2 – 3/2) = 1.5
2. (a) Note : for detailed solution check earlier
question.
Downstream speed, D = 20 km/ 1 hr. – 20 km/hr
Upstream speed, U = 20 km/ 2hr. = 10 km/hr
Speed of the boat in still water , x
= (D + U)/2
= (20 + 10)/2 = 30/2 = 15 km/hr.
3. (c) Speed of the Upstream, U
= 750/675 = 10/9 m/s
Time of downstream
= 15/2 minutes = 450 seconds
(Thus, boat will return in the downstream)
Speed of downstream, D = 750/450 m/s = 5/3 m/s.
Thus, Speed of man in still water = (D + U)/2
= (5/3 + 10/9)/2 = (15 + 10) /(2 × 9) = 25/18
m/s
= 25/18 × 18/5 = 5 km/hr.
4. (c) Speed of boat in still water, x
= 6 km/h
Let speed of the stream = y km/h
Downstream speed = (6 + y) km/h
Upstream speed =
6 – y km/h
According to Question,
3 [(Distance/6 + y) = (Distance/(6 – y)]
3/(6 + y) = 1/(6 – y)
(6 + y) = (18 – 3y)
4y = 12
y = 3
Thus, Speed of stream
= 3 km/h.
5. (b) Speed of upstream, U = 40/8 = 5 km/h
Speedo of Downstream, D
= 36/6 = 6 km/h
Speed of boat in still water, x = (D + U)/2
= (5 + 60)/2 = 11/2 = 5.5 km/h.
6. (c) Speed of man in still water, x = 5 km/h
Speed of currant, y
= 1 km/h
Speed of downstream
= x + y = 5 + 1 = 6 km/h.
Speed of upstream
= x – y= 5 – 1 = 4 km/h
According to the question,
D/6 + D/4 = 1
(2D + 3D)/12 = 1
5D = 12
D = 12/5 = 2.4 km.
7. (c) Speed of motar boat in still water,
x = 36 km/h
Speed of upstream, U
= 56 km/(1 + 3/4) = 56 × 4/7 = 32 km/hr
According to the question,
x – y = U
36 – y = 32
y = 4 km/h
Speed of Downstream, D
= x + y
= 36 + 4
= 40 km/h
Time taken to cover the distance downstream
= 56/40 h
1 hours 24 minutes
8. (b) Speed of man in still water, x
= 9/2 km/hr
Let speed of stream = y km/h
Downstream speed
= (9/2 + y)
Upstream speed = (9/2 – y)
According to the question,
2 [Distance/(9/2 + y)] = Distance/ (9/2 – y)
2/ (9/2 + y) = 1/(9/2 – y)
(2 × 2) /(9 + 2y) = 2/(9 – 2y)
2/(9 + 2y) = 1 / (9 – 2y)
18 – 4y = 9 + 2y
6y = 9
y = 9/6 = 3/2 = 1.5 km/h
9. (c) Since the ratio is given 36 : 5
Let the speed of boat in still water = 36 km/h.
and the speed of the stream = 5 km/h
Downstream speed = 41 km/h
Upstream speed = 31 km/h
Distance = Downstream speed ×
Downstream time = (41 × 31/6) km.
Upstream time
= Distance/ Upstream = [41 × (31/6)]/31 = (41 ×
31)/6 × 3
= 41/6 = 6 hrs. 50 min.
Alternate:
V ∝ 1/T
V1
/V2 = T2/T1
= 36 + 5/(36 – 5) = x/(31/6)
x = 41/6 hours
= 6hrs . 50 min.
10. (d) Downstream speed of boat, D = 15 km/h
Upstream speed of boat, U = 9 km/h
Speed of boat in still water, x = (D + U)/2
= (15 + 9)/2 = 12 km/h
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