QJEEM10Mad43f: JEE Main 2010 Mathematics - Class 11 JEEM10Mad43f Solution: A person is to count 4500 currency notes. Let a n denote the…

Question

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A person is to count 4500 currency notes. Let

a_{n}

denote the number of notes he counts in the

n^{t h}

minute. If

a_{1}

=

a_{2}

= ....=

a_{10}

= 150 and

a_{10}

,

a_{11}

,.... are in an AP with common difference - 2, then the time taken by him to count all notes is

Accepted Answer

Till

10

^th minute number of counted notes

= 1500

3000 = \frac{n}{2} [2 \times 148 + (n - 1) (- 2)]

= n [148 - n + 1]

\Rightarrow

n^{2} - 149 n + 3000 = 0

\Rightarrow n = 125, 24

But

n = 125

is not possible

∴

total time

= 24 + 10 = 34

minutes.

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