Question

Ex. (•) Ajay sharma repays the borrowed amount of 3,25,000 by 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:

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Answer 2

Answer:

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.

$\sf \: So, \: it \: becomes \: Arithmetic \: Progression:$

$\sf \: 30500,29000,27500..$

Here, a = Rs. 30500

$\sf \: d = a_2-a_1=-1500$

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.

$\begin{gathered} \sf \: S_n=\frac{n}{2}(2a+(n-1)d)\\\\ \sf \: 325000=\frac{n}{2}(2\times 30500+(n-1)\times -1500)\\\\ \sf \: \sf \: 325000=\frac{n}{2}(61000-1500n+1500)\\\\ \sf \: 325000\times 2=n(62500-1500n)\\\\ \sf \: 650000=62500n-1500n^2\\\\ \sf15n^2-625n+6500=0\\\\ \sf3n^2-125n+1300\\\\\text{Using Quadratic formula, we get }\\\\ \sf \: \pink{n = \frac{65}{3},20}\end{gathered}$