Question

A man repays a loan of ₹ 3250 by paying ₹305 in the first month

and then decreases the payment by ₹15 every month. How long will

it take to clear his loan?​

Answer 1

Answer:

He takes 20 months

Explanation:

Here, a = 305,

d = 15,

Sn = 3250

Let time required to clear the loan be n months.

Sn=n/2[2a+(n-1)d]

3250=n/2[2×305(n-1)(-15)]

3250×2=n[2×305(n-1)(-15)]

6500=n[610-15n+15]

6500=n[610+15(-15n)]

6500=n[625-15n]

6500=625n-15n^2

15n^2-625n+6500=0

dividing by 5

3n^2-125n+1300=0

splitting middle term

3n-60n-65n+1300=0

3n(n-20)-65(n-20)=0

n-20=0 or 3n-65=0

n=20 or n=65/3

Since n is a natural number,

n≠65/3

n=20

The time required to clear the loan is 20 months.

Hope it is helpful for you.