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Answer :
Final answer:
The question deals with an arithmetic sequence of loan repayments. Using the sum formula of an arithmetic series, the calculation shows it will take approximately 20 months for the man to repay the loan of Rs 3250. So, the correct option is C.
Explanation:
The question involves solving a problem related to loan repayment where a man repays a loan of Rs 3250 by paying Rs. 20 in the first month and increasing the payment by Rs. 15 every subsequent month. This is an arithmetic sequence since the amount of payment increases by a constant value each month.
To find the total number of months required to clear the loan, we need to apply the formula for the sum of an arithmetic series:
- Sn = (n/2) × [2a + (n - 1)d], where:
- Sn is the sum of the first n terms of the series,
- a is the first term of the series,
- d is the common difference,
- n is the total number of terms (or months, in this context).
Given that a = 20, d = 15, and Sn = 3250, we will solve for n to determine the number of months required to repay the loan:
- 3250 = (n/2) × [2×20 + (n - 1)×15],
- Solving for n gives us the equation:
- 3250 = (n/2) × [40 + 15n - 15],
- 3250 = (n/2) × [25 + 15n],
- 6500 = n×[25 + 15n],
- 0 = 15n² + 25n - 6500.
By solving the quadratic equation, we find that n ≈ 20 months. Therefore, he will take approximately 20 months to clear the loan. Hence, the correct option is C. 20 months.
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