Question

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A man has to pay ₹975 in yearly installments, each installment being less than the earlier one by ₹5. The amount of first installment is ₹100.In what time, the entire amount will be paid?

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Answer 1

Answer:

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Explanation:

As given in problem, A=100, D=-5

Formula is:

Sum of AP = n/2 [2a+(n-1)d]

Therefore, 

975 = n/2 [200+(n-1)-5]

1950 = n(200-5n+5)

1950 = 205n-5n^2

5n^2-205n+1950 = 0

n^2-41n+391 = 0

n^2-26n-15n+390 = 0

n(n-26) - 15(n-26) = 0

Hence,

n = 15 or 26.

So,

n = 15 months.

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