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x,y and k

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x,y and k

by swapna » Mon Apr 19, 2010 11:56 am
if x,y and k are positive numbers such that ((x/x+y)(10))+((y/x+y))(20)=k and if x<y, which of the following could be value of k?

a.10
b.12
c.15
d.18
e.30

ans d

can some one help...
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by thephoenix » Mon Apr 19, 2010 10:13 pm
simplifying
10[(x+2y)/(x+y))=10[1+(y/x+y)]
the range for y/(x+y) will be : 0.5<y/(x+y)<1
and the correponding value will be 15<10[1+(y/x+y)]<20
only 18 satisfies the condition
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by ajith » Mon Apr 19, 2010 10:44 pm
swapna wrote:if x,y and k are positive numbers such that ((x/x+y)(10))+((y/x+y))(20)=k and if x<y, which of the following could be value of k?

a.10
b.12
c.15
d.18
e.30

ans d

can some one help...
10x/(x+y) + 20y/(x+y) = 10x/(x+y) + 10y/(x+y) +10y/(x+y) = 10 + 10y/(x+y)

Now x and y are positive so y/(x+y) <1 => 10y/(x+y) <10
also x<y y/(x+y)> 1/2 => 10y/(x+y) > 5

Applying these

15<10x/(x+y) + 20y/(x+y)<20

Only 18 Satisfies this
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