Question

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

Answer 1

Let n be the number of months taken to clear the loan

Amount paid in the first month a = 20

Increased payment in every month d = 15

∴ Amount paid in the second month = 20 + 15 = 35

Amount paid in the third month = 35 + 15 = 50

∴ The sequence of amount paid in every month is 20, 35, 50, …………. which is an A.P with first term a = 20 and common difference = 15

Given S_n = `"n"/2 [2"a" + ("n" - 1)"d"]`

S_n = 3250

3250 = `"n"/2[2 xx 20 + ("n" - 1)15]`

6500 = n[40 + 15n – 15]

6500 = n[25 + 15n]

6500 = 25n + 15n²

1300 = 5n + 3n²

3n² + 5n – 1300 = 0

3n² + 65n – 60n – 1300 = 0

n(3n + 65) – 20(3n + 65) = 0

(n – 20)(3n + 65) = 0

n = 20 = 0 or 3n + 65 = 0

n = 20 or n = `- 65/3`

n = `- 65/3` is not possible

∴ n = 20

Thus, in 20 months the loan is cleared.