A man repays a loan of Rs. 3250 by paying Rs. 20 in the first month and then increases the payment by Rs 15 every month. How long will it take him to clear the loan?

Suppose the loan is cleared in n months. Clearly, the amounts form an A.P. with the first term 20 and the common difference 15.

∴ Sum of the amounts  = 3250

⟹ n/2 {2 × 20 + (n−1) × 15} = 3250

⟹ n/2 (40 + 15n −1 5) = 3250

⟹ n (15n + 25) = 6500

⟹ 152 + 25n − 6500 = 0

⟹ 3n2 + 5n − 1300 = 0

⟹ (n − 20) (3n + 65) = 0

⟹ n = 20 or, n = −65/3  ⟹ n = 20

Hence, the loan is cleared in  months.

Watch the video for more information on arithmetic progression

Further reference

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