Question

A person pays Rs. 975 in monthly instalments, each monthly instalment being less than the former by Rs. 5. The amount of the first instalment is Rs. 100. In what time, will the entire amount be paid?

• A. 12 months
• B. 26 months
• C. 15 months
• D. 18 months

Answer 1

The Correct Option is C

The correct option is (C): 15 months
Explanation:

The order of installments in Rs. is 100, 95, 90, 85 and so on.

The above series forms an A.P. with first term = a = 100 and common difference = d=-5 and total sum = Rs. 975. Let in \(n\) months, total amount is paid.

Sum of an A.P. = \(\frac{n}{2}\)[2a + (n - 1)d] = \(\frac{n}{2}\)[2 × 100 + n (n - 1)(-5)] = 975 
= \(\frac{n}{2}\times\) [200 - 5n+5] = 975 

= 205n - 5\(n^2\) = 1950 
= \(n^2\) - 41n + 390 = 0 
=> (n - 15) (n - 26) = 0 
=> n = 15,26
Now, if n = 26, number of installments will become negative (after 20 installments), hence it is not possible.

\(\therefore\) Total installments = 15 months