# 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

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

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
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

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 2nd 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 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