A person is to count 4500 currency notes. Let andenote the number of notes he counts in the nthminute. Ifa1=a2= .... =a10= 150anda10,a11 ......are in an A.P. with common difference 2, then the time taken by him to count all notes isa)24 minutesb)34 minutesc)125 minutesd)135 minutesCorrect answer is option 'B'. Can you explain this answer?

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A person is to count 4500 currency notes. Let a_n denote the number of notes he counts in the nth 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)
24 minutes
b)
34 minutes
c)
125 minutes
d)
135 minutes

Correct answer is option 'B'. Can you explain this answer?

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A person is to count 4500 currency notes. Let andenote the number of n...

Concept:
Sum of n terms of an A.P. , S_n = n/2(2a+(n−1)d)
Where a = First term, n = Number of terms and, d = Common Difference.

Calculation:
We need to Find the time taken to count all notes.
Since, a₁ = a₂ = .... = a₁₀ = 150.
Thus, The number of notes counted in first 10 minutes = 150 × 10 = 1500
Now, We have left notes = total number of notes - Number of notes counted in first 10 minutes.
i.e. 4500 - 1500 = 3000
Suppose the person counts the remaining 3000 currency notes in n minutes then,
3000 = Sum of n terms of an AP. with first term 148 and common difference -2
3000 = n/2(2(148) + (n − 1)( − 2))
⇒ 3000 = n/2(296−2n + 2)
⇒ 3000 = n/2(298−2n)
⇒ 3000 = n(149 - n)
⇒ 3000 = 149n - n²
⇒ n² - 149n - 3000 = 0
⇒ (n - 125)(n - 24) = 0 (By Separating terms)
⇒ n - 125 = 0 and n - 24 = 0
⇒ n = 125, 24
Since, 125 is not possible.
Thus, n = 24
Therefore,
Total time taken is = 10 + 24 = 34

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A person is to count 4500 currency notes. Let andenote the number of notes he counts in the nthminute. Ifa1=a2= .... =a10= 150anda10,a11 ......are in an A.P. with common difference 2, then the time taken by him to count all notes isa)24 minutesb)34 minutesc)125 minutesd)135 minutesCorrect answer is option 'B'. Can you explain this answer?

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A person is to count 4500 currency notes. Let andenote the number of notes he counts in the nthminute. Ifa1=a2= .... =a10= 150anda10,a11 ......are in an A.P. with common difference 2, then the time taken by him to count all notes isa)24 minutesb)34 minutesc)125 minutesd)135 minutesCorrect answer is option 'B'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about A person is to count 4500 currency notes. Let andenote the number of notes he counts in the nthminute. Ifa1=a2= .... =a10= 150anda10,a11 ......are in an A.P. with common difference 2, then the time taken by him to count all notes isa)24 minutesb)34 minutesc)125 minutesd)135 minutesCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person is to count 4500 currency notes. Let andenote the number of notes he counts in the nthminute. Ifa1=a2= .... =a10= 150anda10,a11 ......are in an A.P. with common difference 2, then the time taken by him to count all notes isa)24 minutesb)34 minutesc)125 minutesd)135 minutesCorrect answer is option 'B'. Can you explain this answer?.

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