Mr. Gulati has a Recurring Deposit Account of `₹ 300` per month. If the rate of interest is `12%` and the maturity value of this account is `₹ 8,100`, find tehe time ( in yesrs ) of this Recurring Deposit Account.

Answer

To solve the problem, we need to find the time (in years) for Mr. Gulati's Recurring Deposit Account given the monthly installment, interest rate, and maturity value.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Monthly installment (P) = ₹300
- Rate of interest (R) = 12% per annum
- Maturity value (M) = ₹8100

2. **Understand the Formula:**
The maturity value of a recurring deposit can be calculated using the formula:
\[ M = P \times n + \text{SI} \]
where SI (Simple Interest) can be calculated as:
\[ \text{SI} = \frac{P \times n \times (n + 1)}{24} \times \frac{R}{100} \]
Here, \( n \) is the number of months.

3. **Express Simple Interest in Terms of Maturity Value:**
Rearranging the first equation gives:
\[ \text{SI} = M - P \times n \]
Substituting the values we have:
\[ \text{SI} = 8100 - 300n \]

4. **Set Up the Equation:**
Now we can set the two expressions for SI equal to each other:
\[ 8100 - 300n = \frac{300 \times n \times (n + 1)}{24} \times \frac{12}{100} \]
Simplifying the right side:
\[ 8100 - 300n = \frac{300 \times n \times (n + 1)}{200} \]
This simplifies to:
\[ 8100 - 300n = \frac{3n(n + 1)}{2} \]

5. **Multiply Through by 2 to Eliminate the Fraction:**
\[ 2(8100 - 300n) = 3n(n + 1) \]
This gives:
\[ 16200 - 600n = 3n^2 + 3n \]

6. **Rearranging the Equation:**
Rearranging gives us a quadratic equation:
\[ 3n^2 + 603n - 16200 = 0 \]

7. **Divide the Entire Equation by 3 for Simplicity:**
\[ n^2 + 201n - 5400 = 0 \]

8. **Factor the Quadratic Equation:**
We need to factor the quadratic equation:
\[ (n - 24)(n + 225) = 0 \]

9. **Solve for n:**
Setting each factor to zero gives:
\[ n - 24 = 0 \quad \text{or} \quad n + 225 = 0 \]
Thus, \( n = 24 \) or \( n = -225 \). Since time cannot be negative, we take \( n = 24 \).

10. **Convert Months to Years:**
Since \( n \) is in months, we convert it to years:
\[ \text{Time in years} = \frac{n}{12} = \frac{24}{12} = 2 \text{ years} \]

### Final Answer:
The time of this Recurring Deposit Account is **2 years**.