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Question

If x1,x2,x3,,xn are n-values of a variable x such that ni=1ui=90 and ni=1Vi=150 where ui=2xi3 and Vi=3xi4, for i = 1, 2, 3, 4, …, n, then the value of n will be

A
30
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B
40
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C
50
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D
60
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Solution

The correct option is A 30
Given: ni=1ui=90 and ni=1Vi=150
where, ui=2xi3 and Vi=3xi4; i = 1, 2, 3, 4, …, n,
Now,ni=1ui=90
ni=1(2xi3)=90
2ni=1xi3n=90
2(x1+x2+.....+xn)3n=90
x1+x2+.....+xn=90+3n2.....(i)
Similarly, ni=1Vi=150
ni=1(3xi4)=150
3ni=1xi4n=150
3(x1+x2+.....+xn)4n=150
x1+x2+.....+xn=150+4n3.....(ii)
From (i) and (ii), we get
90+3n2=150+4n3
270+9n=300+8n
n=30
Hence, the correct answer is option (a).

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