Question

A person is to count 4500 currency notes. Let a_n denote the number of notes he counts in the n^th minute. 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 1

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.