A certain sum of money is given at a certain rate of simple interest for 4 years. Had it been given at 11% higher rate for the same time, it would have fetched ₹1320 more. Find the sum (in ₹).

The correct answer is ₹3000.

We use the Simple Interest (SI) formula:

\mathrm{SI}=\frac{P\times R\times T}{100}

where P = Principal (sum), R = Rate of interest (%), T = Time (years).

Step 1: Understand the problem.
The sum is lent for 4 years. If the rate were 11% higher (i.e., rate increased by 11%), the interest earned would be ₹1320 more. We need to find the Principal P.

Step 2: Set up the equation for the extra interest.
The extra interest earned due to the higher rate is the SI calculated using only the extra rate (11%) for the same time (4 years) on the same Principal P:

\text{Extra SI}=\frac{P\times 11\times 4}{100}

Step 3: Equate to the given extra amount.
We are told this extra interest equals ₹1320:

\frac{P\times 11\times 4}{100}=1320

Step 4: Simplify and solve for P.

\frac{44P}{100}=1320

P=\frac{1320\times 100}{44}

P=\frac{132000}{44}=3000

Step 5: Verify the answer.
For any original rate R, the extra interest at 11% higher rate for 4 years:
Extra SI = (3000 × 11 × 4) / 100 = 132000 / 100 = ₹1320 ✓

This exactly matches the given condition, confirming our answer.

Therefore, the required sum is ₹3000.