correct answer is: b) ₹3200

Explanation

Here,
Amount(A) = ₹3920
Rate(R) =\ 7\large\frac{1}{2} % or \large\frac{15}{2} %
Time(T) = 3 years
Principal(P) =\ ? _{[the sum]}
We know, S.I. =\large\frac{P\times R\times T}{100}
According to the question,
Amount = (Principal + S.I.)
\rightarrow Amount =\left(principle+\large\frac{P\times R\times T}{100}\right)
\rightarrow\;₹3920=\left(p+\large\frac{p\times15\times3}{2\times100}\right)
\rightarrow\;₹3920=\left(p+\large\frac{45p}{200}\right)
\rightarrow\;₹3920=\left(\large\frac{200p\ +\ 45p}{200}\right)
\rightarrow\;₹3920=\left(\large\frac{245p}{200}\right)
\rightarrow\;245p=₹3920\times200 _{[cross multiply]}
\rightarrow\;p=₹\left(\large\frac{3920\;\times\;200}{245}\right)
\rightarrow\;p=₹3200
\therefore The sum is ₹ 3200
Ans: The sum is ₹ 3200.

These precise math questions can also be expressed as:

1. How to calculate the initial sum when it grows to ₹3920 over 3 years at an annual interest rate of 7 ½%?
2. What is the principal amount needed to achieve a total of ₹3920 after 3 years with an annual interest rate of 7 ½%?
3. How to find the principal amount when the interest rate is 7 ½% per annum and the total amount is ₹3920 after 3 years?
4. Finding the principal sum required to yield ₹3920 in 3 years at an interest rate of 7 ½% per annum.