Boats and Streams - Aptitude Questions and Answers Part 2

6. A child swims in still water at 4.5 km/hr. The river is flowing at a rate of 1.5 km/hr. Find the average speed of the child if he swims same distance upstream and downstream.

a. 3 km/hr
b. 3.5 km/hr
c. 4 km/hr
d. 6 km/hr

Answer: c. 4 km/hr

Explanation:

Man's/Boat's Speed = X
Stream/Current/River Speed = Y

∴ Downstream speed = X + Y
Upstream speed = X - Y

∴ X+Y = 4.5+1.5 = 6 km/hr and X-Y = 4.5-1.5 = 3 km/hr
Let distance be D km

Downstream Time	=	Distance	=	D
		Speed		6

Upstream Time	=	D
		3

Average Speed	=	Total Distance	=	D+D	=	6 x 2D	=	4 km/hr
		Time taken		D/6+D/3		3D

7. The time taken by swimmer to swim upstream is 4 hours more than the time he takes to swim downstream. He swims at a speed of 10 km/hr in still water. The stream is flowing gently at 2 km/hr. What is the swimming distance one side?

a. 20 km
b. 72 km
c. 80 km
d. 96 km

Answer: d. 96 km

Explanation:

Man's/Boat's Speed = X
Stream/Current/River Speed = Y

∴ Downstream speed = X + Y
Upstream speed = X - Y

X+Y = 10+2 = 12 km/hr and X-Y = 10-2 = 8 km/hr
Let Time be T hours for downstream
Distance is same
∴ D = D
∴ 12 x T = 8 x (T+4)
∴ T = 8 hours = Time for downstream
Distance = 12km/hr x 8 hours = 96 km

8. Practicing for a competition, a swimmer saw that he could swim 20 km downstream in just 1 hr while it took 2 hrs to swim upstream. Find the speed of the river and that of the swimmer respectively.

a. 4 km/hr ; 16 km/hr
b. 5 km/hr ; 15 km/hr
c. 6 km/hr ; 14 km/hr
d. 8 km/hr ; 12 km/hr

Answer: b. 5 km/hr ; 15 km/hr

Explanation:

Man's/Boat's Speed = X
Stream/Current/River Speed = Y

∴ Downstream speed = X + Y
Upstream speed = X - Y

Downstream Speed	=	Distance covered	=	20	=	20 km/hr
		Time taken		1

Upstream Speed	=	20	=	10 km/hr
		2

X+Y = 20 km/hr and X-Y = 10 km/hr
Adding them we get,
X+Y+X-Y = 30 km/hr
∴ X=15 km/hr = Speed of swimmer in still water
Y=20-15 = 5 km/hr = Speed of river

9. A fisherman can row his boat to the market for 80 km along the stream. For this he takes 1 hour 20 minutes. His son says that, his father’s rowing speed in still water is 45 km/hr. How much time should he take to row the same distance back, against the stream?

a. 2 hours 30 minutes
b. 2 hours 40 minutes
c. 3 hours 10 minutes
d. 4 hours

Answer: b. 2 hours 40 minutes

Explanation:

Man's/Boat's Speed = X
Stream/Current/River Speed = Y

∴ Downstream speed = X + Y
Upstream speed = X - Y

X+Y = (45+Y) km/hr

1 hour 20 minutes = 1 hour	+	20	=	4	hours
		60		3

Downstream Speed	=	Distance covered
		Time taken

∴ 45+Y	=	80	=	60
		4/3

∴ Y = 15 km/hr
X-Y = 45-15 = 30 km/hr

Time taken to go against the stream	=	80	hrs = 2 hours 40 minutes
		30

10. If Madhuri is asked to swim 24 km along the stream and 36 km against the stream, she will take 6 hrs 30 minutes. While, if the distances upstream and downstream are exchanged, she will take 6 hrs. Find the speed of the stream.

a. 2 km/hr
b. 3 km/hr
c. 4 km/hr
d. 6 km/hr

Answer: a. 2 km/hr

Explanation:

Man's/Boat's Speed = X
Stream/Current/River Speed = Y

∴ Downstream speed = X + Y
Upstream speed = X - Y

Downstream time	=	Distance	=	24
		speed		X+Y

Upstream time	=	Distance	=	36
		speed		X-Y

24	+	36	= 6 ½ hours =	13	hours ----------------(1)
X+Y		X-Y		2

Similarly in 2^nd case,

36	+	24	= 6 hours ----------------(2)
X+Y		X-Y

Multiply equation (1) by 2 and equation (2) by 3 and then subtracting equation (1) from (2)

3 x 36	-	2 x 24	= 3 x 6 -	2 x 13
X+Y	-	X+Y	= 3 x 6 -	2

∴	108	-	48	= 5
	X+Y		X+Y

∴ X+Y = 12 km/hr

36	+	24	= 6 -------------Putting value of X+Y in equation (2)
12		X-Y

∴ X-Y = 8 km/hr

(X+Y) - (X-Y) = 12-8 = 4

∴ Y=2 km/hr = Speed of stream

Boats and Streams - Aptitude Questions and Answers Part 2

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