BOATS AND STREAMS SHORTCUTS FOR QUANTITATIVE APTITUDE
1.When a boat is moving in the same direction as the stream or water current, the boat is said to be moving with the stream or moving downstream.
2.Instead of boats in water, it could be a swimmer or a cyclist cycling against or along the wind.
3. When a boat is moving in a direction opposite to that of the stream or water current, the boat is said to be moving against the stream or water current or moving downstream.
4. When the speed of the boat is given, it is the speed of the boat in still water.
5. Speed of the boat against stream or while moving upstream = Speed of the boat in still water - Speed of the stream.
6. Speed of the boat with stream or while moving downstream= Speed of the boat in still water + Speed of the Stream.
7. If 'p' is the speed of the boat down the stream and 'q' is the speed of the boat up the stream, then,
Speed of the boat in still water = (p+q) / 2.
Speed of the boat of the water stream = (p-q) / 2.
Eg 1: A boat travels 36 km upstream in 9 hours and 42 km downstream in 7 hours. Find the speed of the boat in still water and the speed of the water current ?
Ans: Upstream speed of the boat = 36/9 = 4 kmph
Downstream speed of the boat = 42/ 7 = 6kmph.
Speed of the boat in still water = (6+4) / 2.
= 5 kmph
Speed of the water current = (6-4) /2
= 1 kmph
Eg 2: A man can row at 10 kmph in still water. If it takes a total of 5 hours for him to go to a place 24 km away and return, then find the speed of the water current ?
Ans: Let the speed of the water current be y kmph.
Upstream speed = (10- y) kmph
Downstream speed = (10+y) kmph
Total time = (24/ 10+y) + ( 24/10-y) = 5
Hence, 480/ (100-y2 ) = 5
480= 500-5y2
5y2= 20
y2= 4
y = 2 kmph.
8. A man can row x kmph in still waters. If in a stream which is flowing at y kmph, it takes him z hrs to row from A to B and back (to a place and back), then
The distance between A and B = z ( x2 - y2) / 2x.
Eg 3: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. How far is the place?
Ans: Required distance = 1 x ( 62 - ( 1.2)2) kmph
= (36 - 1.44) / 12
= 2.88 km.
9. In the above case, If distance between A and B, time taken by the boat to go upstream and back again to the starting point, speed of the stream are given; then the speed of the boat in still waters can be obtained using the above given formula.
10. A man rows a certain distance downstream in x hours and returns the same distance in y hrs. If the stream flows at the rate of z kmph then,
The speed of the man in still water = z(x+y) / ( y-x) kmph.
EG 4: Ramesh can row a certain distance downstream in 6 hours and return the same distance in 9 hours. If the stream flows at the rate of 3 kmph. Find the speed of Ramesh in still water?
Ans: Ramesh's speed in still water = 3 (9+6) / (9-6)
= 15 kmph.
11. A man rows a certain distance downstream in x hours and returns the same distance in y hours. If the speed of the man in still water z kmph, then
Speed of the stream = z (y-x) / (x+y) kmph.
Eg 5: Ramesh can row a certain distance downstream in x hours and returns the same distance in y hours. If the speed of Ramesh in still water is 12 kmph. Find the speed of the stream?
Ans: Speed of the stream = 12 ( 9-6) / (9+6)
= 2.4 kmph.
