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1.

A person is to count 4500 currency notes. Let andenote the number of notes he counts in the nthminute. If a1 = a2 = ... = a10 = 150 and a10, a11, .... are in an A.P. with common difference –2, then the time taken by him to count all notes is(a) 24minutes(b) 34minutes(c) 125minutes(d) 135minutes

Answer»

Let n – 10 = m
⇒ m × 148 –m(m – 1) = 3000
⇒ m2 – 149m + 3000 = 0
⇒ (m – 24)(m – 125) = 0
∴ m = 24, 125,
giving n = 34, 135
But for n = 135, we have
a135 = 148 + (135 – 1)(–2) = 148 – 268 < 0
But a34 is positive.
Hence, n = 34 is the only answer.
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