Boats and stream - Previous ssc analysis

Types of Questions asked in Previous Exam By SSC

Type 1: When the distance covered by boat in downstream is same as the distance covered by boat upstream. The speed of boat in still water is x and speed of stream is y then ratio of time taken in going upstream and downstream is,

Short Trick:

Time taken in upstream : Time taken in Downstream = (x+y)/(x-y)

Example:  

A man can row 9km/h in still water. It takes him twice as long as to row up as to row down. Find the rate of the stream of the river.

Solution:

Time taken in upstream : Time taken in Downstream = 2 : 1

Downstream speed : Upstream speed = 2 : 1

Let the speed of man = B, & speed of stream = S

B + S : B – S = 2/1

By using Componendo & Dividendo

B/R = 3/1, R = B/3

R = 9/3 = 3km/h
Type 2: A boat cover certain distance downstream in t1 hours and returns the same distance upstream in t2 hours. If the speed of stream is y km/h, then the speed of the boat in still water is:

Short Trick:

Speed of Boat = y [(t2 + t1) / (t2 – t1)]

Example

A man can row certain distance downstream in 2 hours and returns the same distance upstream in 6 hours. If the speed of stream is 1.5 km/h, then the speed of man in still water is

Solution:

By using above formulae

= 1.5 [(6+2) / (6-2)] = 1.5 * (8/4) = 1.5 * 2 = 3km/h

Type 3: A boat’s speed in still water at x km/h. In a stream flowing at y km/h, if it takes it t hours to row to a place and come back, then the distance between two places is

Short Trick:   Distance = [t*(x2 – y2)]/2x

Example

A motor boat can move with the speed 7 km/h. If the river is flowing at 3 km/h, it takes him 14 hours for a round trip. Find the distance between two places?

Solution: By using above formulae

                = [14 * (72 – 32)]/2* 7 = [14 * (49-9)]/2*7

= 14*40/2*7 = 40km

Type 4:  A boat’s speed in still water at x km/h. In a stream flowing at y km/h, if it takes t hours more in upstream than to go downstream for the same distance, then the distance is

Short Trick: Distance = [t*(x2 – y2)]/2y

Example

A professional swimmer challenged himself to cross a small river and back. His speed in swimming pool is 3km/h. He calculated the speed of the river that day was 1km/h. If it took him 15 mins more to cover the distance upstream than downstream, then find the width of the river?

Solution: By using the above formulae

Distance = [t*(x2 – y2)]/2y

= [(15/60) (32 – 12)]/2*1

= [(1/4) * 8] / 2

= 2/2 = 1 km.

Type 5: A boat’s speed in still water at x km/h. In a stream flowing at y km/h, if it cover the same distance up and down the stream, then its average speed is

Short Trick: Average speed = upstream * downstream / man’s speed in still water

Note: The average speed is independent of the distance between the places.

Example

Find the average speed of a boat in a round trip between two places 18 km apart. If the speed of the boat in still water is 9km/h and the speed of the river is 3km/h?

Solution: Average speed = upstream * downstream / man’s speed in still water

Average speed = 6 * 12 / 9 = 8km/h