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A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water at km/h.

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answer is C.

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Detailed Solution

Let boat's speed in calm sea = x km/h
Also stream's velocity = y km/h.
So, boat's upstream speed =

(x - y) km / h

Also, boat's downstream speed =

(x + y) km / h

.
Now we know that,

time = \frac{distance}{speed}

Given,
Distance travelled by Motor boat upstream = 30 km
Distance travelled by Motor boat downstream = 28 km
Time taken for this distance = 7 hours
Also distance travel = 21 km upstream which return in 5 hours.
So,

\frac{30}{x + y} + \frac{28}{x - y} = 7

............ (1)
Also,

\frac{21}{x + y} + \frac{21}{x - y} = 5

............. (2)
Suppose

\frac{1}{x + y} = u

and

\frac{1}{x - y} = v

,
So, equations can be written as,

30 u + 28 v = 7

………….. (3)

21 u + 21 v = 5

……………. (4)
Multiply equation (3) by 21 (4) by 30, so,

630 u + 588 v = 147

………… (5)

630 u + 630 v = 150

……………. (6)
Now subtract equation (5) from (6), to get

42 v = 3

\Rightarrow v = \frac{1}{14}

Put this value in equation (4)

21 u + 21 (\frac{1}{14}) = 5

21 u = 5 - \frac{3}{2}

u = \frac{7}{21 \times 2}

u = \frac{1}{6}

\frac{1}{x + y} = u

and

\frac{1}{x - y} = v

, Thus,,

x + y = 6

……….. (7)

x - y = 14

……. (8)
Add equations (7) and equation (8), to get:

2 x = 20

\Rightarrow x = 10

Thus, speed of boat in still water = 10 km/h.
The Correct option is 3.

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