BEST 5 Shortcuts on Boats and Stream Problems for IBPS PO/Clerk Exams 2017

Cyclist and wind:

Cyclist analogous to boat and wind analogous to stream.

Swimmer and stream:

Swimmer analogous to boat

If speed of boat in still water is ‘b’ km/hr and speed of stream is ‘s’ km/hr,

Speed of boat downstream = (b+s) km/hr, since the boat goes with the stream of water hence its speed increase.

Speed of boat upstream = (b – s) km/hr, the boat goes against the stream of water and hence its speed gets reduced.

Distance = Speed × Time

D = ST

Type 1:

If Ratio of downstream and upstream speeds of a boat is a : b. then ratio of time taken = b : a

Speed of stream = ((a – b)/ ( a + b))× speed in still water.

Speed in still water = ((a + b) /(a – b)) × speed of stream.

Example:

1) A man can row a boat to a certain distanced upstream in 4 hours and takes 3 hours to row downstream the same distance. What is the speed of boat in still water, if the speed of the stream is 2 km/hr?

a) 9km/hr b) 10 km/hr c) 12 km/hr     d) 14 km/hr

Solution:

Ratio of speed downstream and upstream = 3 : 4

Speed of boat in still water = ((4+3) / (4-3)) × 2 = 14 km/hr

2) A man can row a boat 120 km with stream in 5 hours. If speed of the boat is double the speed of the stream, find the speed stream?

1. a) 6 km/hr b) 8 km/hr c) 9 km/hr     d) 12 km/hr

Solution:

Speed of the boat downstream = 120/5 = 24 km/hr

Ratio of speed of boat and stream = 2 : 1, speed of stream = 1/3 *24 = 8 km/hr

Type 2:

1) If a steam boat goes 8 km upstream in 40 minutes and the speed of stream is 5 km/hr, In still water what would be the speed of the boat?

Solution:

Rate of stream = 8 x 60 / 40 = 12 km/h. [convert minutes to hour we multiplying by 60] the speed of stream is 5 km/h

Let speed in still water be x km / hr.

If stream speed 5 km then speed of upstream would be = (x – 5) km/hr

Then, speed upstream = (x – 5) km / hr.

So, x – 5 = 12

x = 12 + 5 = 17 km/hr.

Type 3:

3) Pavi rows in still water with a speed of 4.5 kmph to go to a certain place and to come back. Find his average speed for the whole journey, if the river is flowing with a speed of 1.5 kmph ?

Solution:

Pavi’s speed upstream = 4.5 – 1.5 = 3 kmph

Pavi’s speed downstream = 4.5+1.5 = 6 kmph

Distance = X km

Time Taken in upstream = X/3

Time Taken in downstream = X/6

Average Speed = 2X/(X/3 + X/6 ) = 4 kmph

Type 4:

When a boat’s speed in still water is ‘a’ km/h and river is flowing with a speed of ‘b’ km/h an time taken to cover the same distance downstream, then

Example:

1)A boat’s speed in still water is 10 km/h while river is flowing with speed of 2 km/h and time to cover a certain distance upstream is 4 h more than time taken to cover the same distance downstream. Find the distance.

Solution:

Here, a =10 km/h, b = 2 km/h, T = 4 h

By using formula:

Required distance = [(10^2 – 2^2)/(2×2)]x4

= 96 km

Type 5:

Speed of boat in still water & speed of stream are given. Find average speed of boat that covers certain distance& returns through the same path.

Example:

1) If the speed of boat in still water is 10 km/hr & the speed of stream is 3 km/hr, the boat rows to a place which is 50 km far & returns through the same path. What would be the average speed of boat during the journey?

a) 2 km/hr b) 4.5 km/hr c) 9.1 km/hr   d) 15 km/hr

Solution:

If a boat moves at ‘x’ km/hr speed and covers the same distance up and down in a stream at the speed of ‘y’ km/hr, then average speed is calculated by,