The compound interest on Rs. 1,800 at 10% per annum for a certain period of time is Rs. 378. Find the time in years.
एक निश्चित अवधि के लिए 10% प्रति वर्ष की दर पर Rs. 1,800 पर चक्रवृद्धि ब्याज Rs. 378 है। वर्षों में समय ज्ञात कीजिए।

Options

A. 2.0 वर्ष
B. 2.8 वर्ष
C. 30 वर्ष
D. 2.5 वर्ष

Explanation

To find the time in years for the given compound interest, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 1,800
- Rate (R) = 10% per annum
- Compound Interest (CI) = Rs. 378

### Step 2: Calculate the total amount (A)
The total amount (A) after the interest is added can be calculated as:
\[ A = P + CI \]
Substituting the values:
\[ A = 1800 + 378 = 2178 \]

### Step 3: Use the compound interest formula
The formula for compound interest is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^N \]
Where:
- A = Total amount after interest
- P = Principal amount
- R = Rate of interest per annum
- N = Time in years

### Step 4: Substitute the known values into the formula
Substituting the values we have:
\[ 2178 = 1800 \left(1 + \frac{10}{100}\right)^N \]
This simplifies to:
\[ 2178 = 1800 \left(1 + 0.1\right)^N \]
\[ 2178 = 1800 \left(1.1\right)^N \]

### Step 5: Divide both sides by 1800
To isolate the term with N:
\[ \frac{2178}{1800} = (1.1)^N \]
Calculating the left side:
\[ \frac{2178}{1800} = 1.21 \]
So we have:
\[ 1.21 = (1.1)^N \]

### Step 6: Rewrite 1.21 as a power of 1.1
We know that:
\[ 1.1^2 = 1.21 \]
Thus, we can equate the powers:
\[ (1.1)^N = (1.1)^2 \]
This implies:
\[ N = 2 \]

### Conclusion
The time in years (N) is 2 years.