What sum (in ₹) will earn a simple interest of ₹1680 in 3 years at 8% per year…

Concept — recovering the principal from the simple-interest relation. Simple interest is charged only on the original principal and never on interest already earned, so the same amount of interest accrues in every year of the term. For a principal P, an annual rate of R% and a time of T years, the four quantities are tied together by one relation: SI = P × R × T / 100. Because it is a single equation, any one quantity can be recovered once the other three are known; rearranging it for the principal gives P = SI × 100 / (R × T).

Application — solving this problem.

1. List what the question supplies: SI = ₹1680, R = 8% per year and T = 3 years, with the principal P unknown.

2. Substitute these into SI = P × R × T / 100, giving 1680 = P × 8 × 3 / 100.

3. Simplify the right-hand side: 8 × 3 = 24, so 1680 = 24P / 100, that is 1680 = 0.24P.

4. Solve for the principal: P = 1680 × 100 / 24 = 168000 / 24 = 7000, so the sum is ₹7000.

Cross-check and common slips. Substituting the principal back reproduces the given interest: 7000 × 8 × 3 / 100 = 7000 × 0.24 = ₹1680. A quick sense-check works too — over 3 years at 8% per year the interest is 24% of the principal, so the principal must be a little over four times the interest, and 1680 × 100 / 24 is indeed 7000. Two slips are common here: multiplying by 24/100 instead of dividing turns the answer into ₹403.2, and halving or doubling the R × T product (using 48 or 12 in place of 24) gives ₹3500 or ₹14000.