A boat goes 12 km upstream and 40 km downstream in 8hrs. It can go 16 km upstream and 32km downstream at the same time. Find the speed of the boat in still water and the speed of the stream.

Chapter/Topic: Pair Of Linear Equations In Two Variables

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Speed of boat in still water = 9km/hr and speed of stream 6km/hr.

Speed of boat in still water = 6km/hr and speed of stream 2km/hr.

Speed of boat in still water = 14km/hr and speed of stream 32km/hr.

Speed of boat in still water = 7km/hr and speed of stream 23km/hr.

answer is B.

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Detailed Solution

Let,Speed of the boat in still water be x km/hr
Speed of the stream be y km/hr
Speed of boat in downstream = (x+y) km/hr
Speed of boat in upstream = (x-y )km/hr
According to given problem
Time taken to cover 12km upstream =

\frac{12}{(x - y)}

hrs
Time taken to cover 40km downstream =

\frac{40}{(x + y)}

hrs
But, the total time taken =8hr
=

\frac{12}{(x - y)}

\frac{40}{(x + y)}

hrs=8.........(1)
Time taken to cover 16km upstream =

\frac{16}{(x - y)}

hrs
Time taken to cover 32km downstream =

\frac{32}{(x + y)}

hrs
Total time taken = 8hr
=

\frac{16}{(x - y)}

\frac{32}{(x + y)}

hrs=8.......(2)
Put ,

\frac{1}{(x - y)}

=p and

\frac{1}{(x + y)}

=q
Hence we get equation
12p + 40q = 8....(3)
16p + 32q = 8....(4)
Furthur simplyfying the eq we get
3p + 10q = 2..........(3)
2p + 4q = 1.........(4)
Multiply eq (3) by 2 and eq (4) by 3
6p + 20q = 4...........(3)
6p + 12q = 3............(4)
subtracting eq (4) from eq(3) we get
q=

\frac{1}{8}

and we get p=

\frac{1}{4}

Hence p=

\frac{1}{(x - y)}

\frac{1}{4}

and q=

\frac{1}{(x + y)}

\frac{1}{8}

x-y = 4..(5)
x+y= 8....(6)
Solving equation(5) and (6) we get x = 6 and y=2
Hence speed of boat in still water = 6km/hr and speed of stream 2km/hr.
Hence, Option (2) is the correct answer.

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