Streams Aptitude solved Examples - ObjectiveBooks

# Streams Aptitude solved Examples

Question No. 01
A man can row three quarter of a km against the stream in 11¼ min and return in 7½ min. The speed of the man in still water is?
(A) 5 km/hr
(B) 7 km/hr
(C) 7.5 km/hr
(D) None of these
Explanation:
Upstream speed = (3/4)/[(45/4) × 60] = (3 × 4 × 60)/(4 × 45) = 4 km/hr
Downstream speed = (3/4)/[(15/2) × 60] = (3 × 2 × 60)/(4 × 15) = 6 km/hr
∴ Speed in still water = (4 + 6)/2 = 5 km/hr.

Question No. 02
A boat covers 24 km upstream and 36 km downstream in 6 hrs, while it covers 36 km upstream and 24 km downstream in 6½ hrs. The average speed of current is?
(A) 1.5 km/hr
(B) 1 km/hr
(C) 2 km/hr
(D) 2.5 km/hr
Explanation:
Upstream speed of boat = [(24 × 24) - (36 × 36)]/[(24 × 6) - (36 × 6.5)] = 8 km/hr
Downstream speed of boat = [(24 × 24) - (36 × 36)]/[(24 × 6.5) - (36 × 6)] = 12 km/hr
∴ Speed of current = (12 - 8)/2 = 2 km/hr.

Question No. 03
A man rows upstream 16 km and downstream 28 km, taking 5 hrs each time. The velocity of the current is?
(A) 2 km/hr
(B) 1.2 km/hr
(C) 2.4 km/hr
(D) 3.6 km/hr
Explanation:
Upstream speed = (16/5) km/hr
Downstream speed = (28/5) km/hr
Velocity of current = [(28/5) - (16/5)]/2 = 12/10 = 1.2 km/hr.

Question No. 04
If a man’s rate with the current is 12 km/hr and the rate of the current is 1.5 km/hr. Then the man’s rate against the current in km/hr will be:
(A) 18 km/hr
(B) 22 km/hr
(C) 6 km/hr
(D) 9 km/hr
Explanation:
Man’s rate against current = Man’s rate against current - (2 × Rate of current)
= 12 - (2 × 1.5) = 9 km/hr.

Question No. 05
The current of a stream runs at 1 km/hr. A motor boat goes 35 km upstream and back again to the starting point in 12 hrs. The speed of the motor boat in still water is?
(A) 6 km/hr
(B) 9 km/hr
(C) 12 km/hr
(D) 14 km/hr
Explanation:
35 = 12 (α² - 1²)/2α
=> 6α² - 36α + α - 6 = 0
=> α = 6   or -1/6
We neglected -ve sign, therefore
Speed of boat in still water = 6 km/hr.

Question No. 06
A man can row 9⅓ km/hr in still water and he finds that it takes him thrice as much time to row up than as to row down the same distance in river. The speed of the current is?
(A) 6 km/hr
(B) 7½ km/hr
(C) 4⅔ km/hr
(D) None of these
Explanation:
Let, the speed of current = α km/hr
Then, 28/3 + α = 3 [(28/3) - α]
or,        4α = (2 × 28)/3
or,          α = (14/3) km/hr = 4⅔ km/hr.

Question No. 07
A man can row at 5 km/hr in still water and the velocity of the current is 1 km/hr. It takes him 1 hr to row to a place and back. How far is the place?
(A) 2.4 km
(B) 2.3 km
(C) 2.8 km
(D) 2.5 km