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.
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