Question

Ajay sharma repays the borrowed amount of ` 3,25,000by paying ` 30500

in the first month and then decreases the payment by ` 1500 every month. How long will it take to clear his amount?​

Answer 1

⋆Answer

It will take 20 month to clear the amount.

Step-by-step explanation:

Since we have given that

Total borrowed amount of money that Ajay repays = Rs. 325000

Amount he paid in the first month = Rs. 30500

Then each month the payment will decrease by Rs. 1500.

So, it becomes Arithmetic Progression:

30500,29000,27500..............

Here, a = Rs. 30500

d =

We will find the number of terms i.e. number of years it will take to clear the amount .

We will use the formula for "Sum ":

so, it will take 20 month to clear the amount as it satisfies the above equation completely.

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Answer 2

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Solution : Let the time required to clear the amount be n months. The monthly payment

decreases by ` 1500. Therefore the payments are in A.P.

First term = a = 30500, d = -1500

Amount = Sn= 3,25,000

Sn = n2 [2a+(n-1)d]

3,25,000= n2 [2 ´ 30500+(n-1)d]

= n2 [2 ´ 30500 - 1500n + 1500]

3,25,000 = 30500n - 750n2 +750n

750n2 -31250n + 325000 = 0

divide both sides by 250.

3n2 -125n + 1300 = 0

3n2 -60n - 65n + 1300 = 0

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

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

n - 20 = 0 , 3n - 65 = 0

n = 20 or n = 65

3 = 21

In an A.P. n is a natural number.

:n ¹65

3 \ n = 20

(Or, after 20 months, S.20 = 3,25,000 then the total amount will be repaid. It is not required to think about further period of time.)

:To clear the amount 20 months are needed.