Boats & Streams Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 1 EXERCISES
The following question based on Boats & Streams topic of quantitative aptitude
(a) 1 : 4
(b) 1 : 2
(c) 1 : 3
(d) 2 : 3
The correct answers to the above question in:
Answer: (a)
Let speed of boat in still water = x km/hr
Let speed of stream = y km/hr
Let distance covered = d km
∴ $d/{x+y}=45/60=3/4$ …(1)
$d/{x-y}=75/60=5/4$ …(2)
Form (1) & (2),
${x-y}/{x+y}=3/5 ⇒5x-5y=3x+3y$
⇒2x=8y ⇒ $y/x=1/4 $
∴ ratio of speed of the stream to boat in still water = 1 : 4
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Question : 1
A steamer goes downstream from one part to another in 4 hours. It covers the same distance upstream in 5 hours. If the speed of stream is 2 km/hr, the distance between the two ports is
a) 68 km
b) 45 km
c) 64 km
d) 80 km
Answer »Answer: (d)
Let the distance between the two parts = 'x' km
Let the speed of steamer in still water = 'y' km/hr
∴ $x/{y+2}$=4 ⇒x=4y+8 ….(1)
$x/{y-2}$=5⇒x=5y-10 …..(2)
From (1) and (2)
4y+8=5y-10
⇒ y = 18
∴ From (1)
x = 4 × 18 + 8 = 80 km.
Question : 2
A boat takes 19 hours for travelling downstream from point A to point B and coming back to point C, mid way between A and B. If the velocity of the stream is 4 km/hr and the speed of the boat in still water is 14 km/hr. then the distance between A & B is
a) 180 km
b) 200 km
c) 160 km
d) 190 km
Answer »Answer: (a)
Downstream speed = 14 + 4 = 18 km/hr
Upstream speed = 14 – 4 = 10 km/hr
Let the distance between A and B = 'x' km
∴ $x/18+{x/2}/10=19$
∴ $x/18+x/20=19$
${10x+9x}/180=19$
${19x}/180=19$ ⇒ x=180km
Question : 3
A man rows upstream 24 km and downstream 36 km taking 6 hours each. Find the speed of current.
a) 1.5 km/h
b) 0.5 km/h
c) 1 km/h
d) 2 km/h
Answer »Answer: (c)
Let man's rowing speed in still water = x km/hr
Let speed of current = y km/hr
Downstream speed = x + y = $36/6$ = 6 …(1)
Upstream speed = x – y = $24/6$ = 4 …(2)
(1) – (2)
2y = 2 ⇒ y = 1
∴ speed of current = 1 km/hr.
Question : 4
If a man’s rate with the current is 12 km/hr. and the rate of the current is 1.5 km/hr, then man’s rate against the current is –
a) 5.25 km/hr
b) 9 km/hr
c) 6.75 km/hr
d) 7.5 km/hr
Answer »Answer: (b)
Let the rate against the current be x km/hr. Then,
${12-x}/2$ = 1.5 ⇒12 – x = 3 ⇒ x = 9 km / hr
Question : 5
A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is
a) 2 : 1
b) 3 : 1
c) 4 : 3
d) 3 : 2
Answer »Answer: (b)
Let speed in downstream = (x + y)
Speed in upstream = (x – y)
∴ (x + y) = 2 (x – y)
x = 3y
x : y = 3 : 1
Question : 6
The speed of a boat in still water is 8 km/hr. It can travel 20 km downstream at the same time as it can travel 12 km upstream, the rate of stream (in kmph) is
a) 2.5
b) 0.5
c) 2
d) 2.75
Answer »Answer: (c)
Let rate of stream = x kmph
∴ $20/{8+x}=12/{8-x}$
160 – 20x = 96 + 12x
64 = 32x
x = 2
∴ Rate of stream = 2 kmph
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