Question

A man repays a debt of 4860 by paying 30 in the first month and then increases
the amount by 15 every month. How long will it take him to clear the debt (Assume
that no interest is charged?)​

Answer 1

Answer:

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

∴ Sum of the amounts =3250

⟹

2

n

{2×20+(n−1)×15}=3250

⟹

2

n

(40+15n−15)=3250

⟹n(15n+25)=6500

⟹15

2

+25n−6500=0

⟹3n

2

+5n−1300=0

⟹(n−20)(3n+65)=0

⟹n=20 or, n=−

3

65

⟹n=20 [∵n



=

3

65

]

Thus, the loan is cleared in 20 months.