Question

A man repays a loan of rupees 3250 by paying rupees 20in the first month and then increases the payment by rupees 15 every month how long will it take him to clear a loan​

Answer 1

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