16.  A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. Find the speed of the current.


1 km/hr
2 km/hr
3 km/hr
4 km/hr


Answer

 Option

First of all, we know that speed of current = 1/2(speed downstream - speed upstream) [important] So we need to calculate speed downstream and speed upstream first. Speed = Distance / Time [important] Speed upstream =(15334)km/hr=15×415=4km/hrSpeed Downstream = (5212)km/hr=5×25=2km/hrSo speed of current = 12(4−2)=1km/hr

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17.   If Rahul rows 15 km upstream in 3 hours and 21 km downstream in 3 hours, then the speed of the stream is


5 km/hr
4 km/hr
2 km/hr
1 km/hr


Answer

 Option

Rate upstream = (15/3) km/ph Rate downstream (21/3) km/ph = 7 km/ph. Speed of stream (1/2)(7 - 5)km/ph = 1 km/ph

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18.  A man rows 750 m in 675 seconds against the stream and returns in 7 and half minutes. His rowing speed in still water is


4 kmph
5 kmph
6 kmph
7 kmph


Answer

 Option

Rate upstream = (750/675) = 10/9 m/sec Rate downstream (750/450) m/sec = 5/3 m/sec Rate in still water = (1/2)*[(10/9) + (5/3)] m/sec. = 25/18 m/sec = (25/18)*(18/5) km/ph = 5 km/ph

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19.  At his usual rowing rate, A can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his 24 -mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. what is the speed of the current in miles per hour?


1 1/3
1 2/3
2 1/3
2 2/3


Answer

 Option

Let the speed still in water be x mph and the speed of the current be y mph. Speed upstream = (x-y): Speed downstream = (x+y) 12/(x-y) -12/(x+y) = 6 <=> 6(x^2 - y^2 = 24y ,<=> x^2-y^2 = 4y <=> x^2 = (4y+y^2)........(1) And 12/(2x-y) - 12/ (2x+y) = 1 <=> 4x^2 - y^2 = 24y <=> x^2 = 24y+y^2/4 .........(2)

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20.  A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream in 6 1/2 hours. the velocity of the current is?


1 km/hr
1.5 km/hr
2 km/hr
2.5 km/hr


Answer

 Option

Let rate upstream = x km/hr and rate downstream =y km/hr. Then, 24/x+36/y =36 ...............(1) and 36/x+24/y = 13/2 ...............(2) Adding (1) and (2) we get : 60(1/x+1/y) = 25/2 or 1/x+1/y = 5/24 ....................(3) subtracting (1) from (2) we get :12(1/x-1/y) =1/2 or 1/x-1/y=1/24 .....................(4) Adding (3) and (4) we get : 2/x = 6/24 or x =8. so, 1/8+1/y =5/24 <=> 1/y = (5/24-1/8) = 1/12 <=> y =12. therefore speed upstream = 8 km/hr, speed downstream = 12 km/hr. Hence, rate of current = 1/2(12-8) km/hr = 2 km/hr.

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