Find the sum on which the compound interest for 3 years at 10% per annum amounts to Rs 1,655

Answer

To find the sum (principal) on which the compound interest for 3 years at 10% per annum amounts to Rs 1,655, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Compound Interest (CI) = Rs 1,655
- Time (n) = 3 years
- Rate of Interest (r) = 10% per annum

2. **Use the Compound Interest Formula**:
The formula for the amount (A) after n years with compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
where:
- A = Total amount after n years
- P = Principal amount (the sum we need to find)
- r = Rate of interest
- n = Time in years

3. **Relate Amount to Principal and Compound Interest**:
Since the compound interest is given, we can express the amount (A) as:
\[ A = P + CI \]
Substituting the value of CI:
\[ A = P + 1655 \]

4. **Substitute into the Formula**:
Now we can substitute A in the compound interest formula:
\[ P + 1655 = P \left(1 + \frac{10}{100}\right)^3 \]
Simplifying the right side:
\[ P + 1655 = P \left(1 + 0.1\right)^3 = P \left(1.1\right)^3 \]

5. **Calculate \( (1.1)^3 \)**:
\[ (1.1)^3 = 1.1 \times 1.1 \times 1.1 = 1.331 \]
Thus, we have:
\[ P + 1655 = P \times 1.331 \]

6. **Rearranging the Equation**:
Rearranging gives:
\[ P \times 1.331 - P = 1655 \]
Factoring out P:
\[ P(1.331 - 1) = 1655 \]
This simplifies to:
\[ P(0.331) = 1655 \]

7. **Solve for Principal (P)**:
\[ P = \frac{1655}{0.331} \]
Calculating this gives:
\[ P \approx 5000 \]

8. **Final Calculation**:
To find the exact value:
\[ P = \frac{1655 \times 1000}{331} \approx 1000 \]

### Final Answer:
The principal amount (sum) is Rs 1000.