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Question

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. If x represents the speed of the boat in still water in km/hr and y represents the speed of the stream in km/hr, then _________.

A
x+y=11,xy=5
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B
x+y=5,xy=11
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C
x+y=6,xy=10
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D
x+y=10,xy=6
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Solution

The correct option is A x+y=11,xy=5
Speed of boat in still water =x
Speed of stream =y

Speed of boat upstream =xy
Speed of boat downstream =x+y

Thus,
30xy+44x+y=10

Let 1xy=a and 1x+y=b
So we have,
30a+44b=10......(1)
Similarly,
40a+55b=13......(2)

Multiplying (1) by 4 and (2) by 3, we get
120a+176b=40......(3)
120a+165b=39......(4)

Subtracting (4) from (3), we get
b=111
x+y=11
Putting b=111 in (1), we get
30a+4=10
a=15
xy=5

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