Question

A man repays a loan of rs3250 by paying rs305 in the fiest month and then decreases the payment by rs15 every month. How long will it take to clear his loan​

Answer 1

SO NUMBER = 20

$the \: man \: will \: repay \: the \: loan \: in \: 20 \: months$

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Answer 2

Answer:

20 Months

Step-by-step explanation:

Ammount to be paid=3250=Sn

First payment=305=A1

Difference=-15

Now,

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

=>3250=n/2[2*305+(n-1)*(-15)]

=>6500=n[610-15n+15]

=>6500=610n-15n^2+15n

=>-15n^2+625n-6500=0

Dividing by 5

=>-3n^2+125n-1300=0

On comparing with ax^2+bx+c=0,

a=-3,b=125,c=-1300

now,b^2-4ac=125^2- 4*(-3)*(-1300)

=15625-4*(+3900)

=15625-15600

=25

Since b^2-4ac >0,

roots are real and distinct

=>X=(-b+√b^2-4ac)/2a or (-b-√b^2-4ac)/2a

=>X=(-125+√15625-15600)/2*(-3) or (-125-√15625-15600)/ 2*(-3)

=>X=(-125+√25)/-6 or (-125-√25)/-6

=>X=(-125+5)/-6 or (-125-5)/-6

=>X=(-120)/(-6) or (-130)/(-6)

=>X=20 or 65/3 Months

But, Months can't be in a fraction

Hence ,

X=20 months

i.e.

n=20

Therefore,

He will pay back the loan in 20 Months