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Question

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 in km/h.

A
3
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B
15
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C
10
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D
11
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Solution

The correct option is D 10
Let the speed of the boat in still water be x km/h and speed of the stream is y km/h.

Therefore, speed of the boat while upstream is (xy) km/h and speed of the boat while downstream is (x+y) km/h

As we know that speed=distancetime, therefore, time=distancespeed

It is given that the motor boat can travel 30 km upstream and 28 km downstream in 7 hours and also it can travel 21 km upstream and return in 5 hours, thus,

30x+y+28xy=7.............(1)21x+y+21xy=5.............(2)

Let 1x+y=u and 1xy=v, then the equations (1) and (2) becomes:

30u+28v=7..........(3)
21u+21v=5..........(4)

Multiplying equation (3) by 21 and equation (4) by 30 we get,

630u+588v=147..........(5)
630u+630v=150..........(6)

Now subtracting equation (5) from equation (6), we get


42v=3
v=114

Substitute the value of v in equation (4) then, u=16

Since 1x+y=u and 1xy=v, therefore,

x+y=6..........(7)
xy=14..........(8)

Adding equations (7) and (8), we get:

2x=20
x=10
Hence, the speed of the boat in still water is 10 km/h.

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