If Cl on some amount for 2 years at 15% rate is 3225 then find the amount?

Options

A. ₹ 10500
B. ₹ 10000
C. ₹10100
D. ₹ 10750

Answer

To find the principal amount given the compound interest (CI), we can follow these steps:

### Step 1: Understand the given information
We know:
- Compound Interest (CI) = 3225
- Time (T) = 2 years
- Rate of Interest (R) = 15%

### Step 2: Convert the rate of interest to a fraction
The rate of interest can be expressed as a fraction:
\[ R = \frac{15}{100} = \frac{3}{20} \]

### Step 3: Determine the ratio of Principal (P) to Amount (A)
For 1 year, the ratio of Principal to Amount is:
\[ P : A = 20 : 23 \]
This means for every 20 units of Principal, the Amount after 1 year is 23 units.

### Step 4: Extend the ratio for 2 years
For 2 years, the ratio of Principal to Amount becomes:
\[ P : A = 20^2 : 23^2 = 400 : 529 \]

### Step 5: Calculate the total units for CI
The total units of CI can be calculated as:
\[ CI = A - P \]
From the ratio, we can see:
\[ A = 529 \text{ units} \]
\[ P = 400 \text{ units} \]
Thus,
\[ CI = 529 - 400 = 129 \text{ units} \]

### Step 6: Find the value of 1 unit
We know that 129 units correspond to the CI of 3225. Therefore, we can find the value of 1 unit:
\[ 1 \text{ unit} = \frac{3225}{129} \]

### Step 7: Calculate the value of 1 unit
Calculating the above expression:
\[ 1 \text{ unit} = 25 \]

### Step 8: Find the Principal amount
Now, we can find the value of the Principal amount (400 units):
\[ P = 400 \text{ units} = 400 \times 25 = 10000 \]

### Final Answer
The principal amount is **10,000**.

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