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A boat goes 16 km upstream and 24 km downstream in 6 hours. Also, it covers 12 km upstream and 36 km downstream in the same time. Find the speed of the boat in still water and that of the stream.

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Boat

= 8 km / hr

and

Stream = 4 km / hr

Boat

= 3 km / hr

and Stream

= 4 km / hr

Boat

= 9 km / hr

and Stream

= 4 km / hr

Boat

= 4 km / hr

and Stream

= 4 km / hr

answer is A.

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Detailed Solution

It is given that,
Boat goes 16 km upstream and 24 km downstream in 6 hours and it covers 12 km upstream and 36 km downstream in the same time.
Let the stream's speed be

y km / hr

and the boat's speed in still water be

x km / hr

.
Therefore,
Speed upstream = (x – y) km/hr
Speed downstream = (x + y) km/hr.
According to question,
Time taken to cover 16 km upstream =

16 (x - y) hr

.
Time Taken to cover 24 km downstream =

24 (x + y)

hr.
Total Time Taken to cover both distance = 6 hr.
Therefore,

16 (x - y) + 24 (x + y) = 6

.…... (1)
And
Time taken to cover 12 km upstream =

12 (x - y)

hr.
Time Taken to cover 36 km downstream =

36 (x + y)

hr.
Total Time Taken to cover both distance = 6 hr.
Therefore,

12 (x - y) + 36 (x + y) = 6

.…... (2)
Putting

1 x − y = u and 1 x + y ​ ​ ​ ​ = v

.
Then the equations become,

16 u + 24 v = 6 … … . 3 12 u + 36 v = 6 … … . 4

Multiplying equation (3) by 4 and equation (4) by 3,

48 u + 72 v = 18 … … . 5 48 u + 144 v = 24 … … . 6

Subtracting equation (5) from equation (6), we get:

v = \frac{1}{12}

Using the value of

v

to solve equation (4) will yield the value of u,

12 u + 36 v = 6 12 u + 36112 = 6 12 u + 3 = 6 12 u = 6 − 3 12 u = 3 u = 312 u = 14

Put the value of u and v in

1 x − y = u and 1 x + y ​ ​ ​ ​ = v

we get,

1 x − y = 14 and 1 x + y ​ ​ ​ ​ = 112

So,

1 x − y = 14 ⇒ x − y = 4 ... (7) and 1 x + y ​ ​ ​ ​ = 112 ⇒ x + y = 12 ... (8)

From equations (7) and (8) we get,

x = 8 and y = 4

So, the speed of the boat in still water is 8km/hr and the speed of the stream is 4km/hr.
Hence, option (1) is correct.

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