Problem:
At a rate of 6% per annum simple interest, after 9 months the amount due is ₹20900. Find its present value.

Solution:

Step 1: Find the interest rate per month
We are given an annual interest rate of 6%, so first we need to find the monthly interest rate. We can do this by dividing the annual rate by 12 (since there are 12 months in a year).

6% / 12 = 0.5% per month

Step 2: Find the time in years
We are given that the interest is for 9 months. To find the time in years, we need to divide 9 by 12.

9 / 12 = 0.75 years

Step 3: Find the interest
We can now use the formula for simple interest to find the interest on the amount:

I = P * r * t

where P is the principal (the present value), r is the interest rate per time period, and t is the time in years.

I = P * 0.5% * 0.75
I = 0.00375P

The interest is ₹0.00375P.

Step 4: Find the present value
We know that after 9 months, the amount due is ₹20900. This amount includes the principal and the interest.

A = P + I

Substituting I from step 3, we get:

20900 = P + 0.00375P

Simplifying this equation, we get:

20900 = 1.00375P

Dividing both sides by 1.00375, we get:

P = ₹20798.51

Therefore, the present value of the amount is ₹20798.51.

Conclusion:
The present value of the amount is ₹20798.51.