Question

27. 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.
lit 207 into three parts such that these are in AP and the product of two smaller​

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

]

Answer 2

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

⟹ 2n {2×20+(n−1)×15}=3250

⟹ 2 (40+15n−15)=3250

⟹n(15n+25)=6500

⟹15² +25n−6500=0

⟹3n² +5n−1300=0

⟹(n−20)(3n+65)=0

⟹n=20 or, n=− 365

⟹n=20 [∵n= 365 ]

Thus, the loan is cleared in 20 months.