A person is to count 4500 currency notes. Let an denote the numberof notes he counts in the nth minute. If `a_1=a_2=. . . . . .=a_(10)=150`and `a_(10)a_(11). . . . . .`are in A.P. with commondifference 2 then the time taken by him to count all notes is(1) 34 minutes(2) 125 minutes (3) 135minutes (4) 24 minutes

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1.	A person is to count 4500 currency notes. Let an denote the numberof notes he counts in the nth minute. If `a_1=""a_2="". . . . . .""=""a_(10)=""150`and `a_(10),""a_(11),"". . . . . .`are in A.P. with commondifference 2, then the time taken by him to count all notes is(1) 34 minutes(2) 125 minutes (3) 135minutes (4) 24 minutes
Answer» first 10 minutes=`150 xx 10 = 1500` `148 + 146 + 144 + .....` `4500 = 1500 + n/2(296 + (n-1)(-2)) ` `3000 = (296n - 2n^2 + 2n)/2` `2n^2 + 298n + 6000= 0` `n^2 - 149n + 3000 = 0` `n^2 - (125 + 24)n + 125 xx 24 = 0` `(n-24)(n-125) = 0` `n=24 or 125` `n ` cannot be 125 so `n=24` total =`24+ 10 = 34`minutes Answer

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