BOATS SET4

1. Man can row 30km upstream & 44km downstream in 10 hrs. Also he run 40km upstream & 55km downstream in 13 hrs. Find the rate of the current & the speed of the man in still water ?
A) 3 & 8 km/hr
B) 2 & 5 km/hr
C) 1 & 3 km/hr
D) None of the above
Ans. A
Upstream Downstream time
30 44 10
40 55 13
Upstream = 30*55 – 40*44 / 44*13 – 55*10 = 5
Downstream = 30*55 – 40*44 / 30*13 – 40*10 = 11
Therefore, Rate of current = 11-5/2 = 3 km/hr
Speed of the man = 11+5/2 = 8 km/hr

2. A motor boat takes 2 hrs to travel a distance of a 9km down the current & it takes 6 hrs. to travel the same distance against the current. The speed of the boat(in km/hr) in still water & that of the current are
A) 3,2
B) 3,1
C) 3.5,2.5
D) 3,1.5
Ans. D
Let speed of boat in still water be x km/hr & speed of current be y km/hr
9/x+y = 2
& 9/ x-y =6
X+y=9/2
x-y = 9/6 = 3/2
therefore, x=3 & y=1/2 km/hr

3. A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find
the time taken by the boat to cover distance of 84 km downstream.
A) 4 hours
B) 5 hours
C) 6 hours
D) 7 hours
Ans. A
Speed downstream = (16 + 5) = 21 kmph

Time = distance/speed = 84/21 = 4 hours

4. A man can row at 5 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour
to row to a place and come back. how far is that place.
A) 0.4 km
B) 1.4 km
C) 2.4 km
D) 3.4 km
Ans. C
Let the distance is x km
Rate downstream = 5 + 1 = 6 kmph
Rate upstream = 5 – 1 = 4 kmph
then
x/6 + x/4 = 1 [because distance/speed = time]=> 2x + 3x = 12
=> x = 12/5 = 2.4 km

5. The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is
A) 1.6 km
B) 2 km
C) 3.6 km
D) 4 km
Ans. C
Speed downstreams =(15 + 3)kmph
= 18 kmph.
Distance travelled = (18 x 12/60)km
= 3.6km

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